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ISEE Middle Level Math : ISEE Middle Level (grades 7-8) Mathematics Achievement

Study concepts, example questions & explanations for ISEE Middle Level Math

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All ISEE Middle Level Math Resources

6 Diagnostic Tests 303 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #291 : How To Find The Square Root

$4\sqrt{144} + 3\sqrt{64} =$ $\displaystyle 4\sqrt{144} + 3\sqrt{64} =$

Possible Answers:

x = 62 $\displaystyle x = 62$

x = 72 $\displaystyle x = 72$

x =64 $\displaystyle x =64$

x = 40 $\displaystyle x = 40$

Correct answer:

x = 72 $\displaystyle x = 72$

Explanation:

First find the square root of 144; which is 12. Then multiply:

$4 \times 12 = 48$ $\displaystyle 4 \times 12 = 48$

Then find the square root of 64, which is 8. Then multiply:

$8 \times 3 = 24$ $\displaystyle 8 \times 3 = 24$

Then add those two numbers together:

$\displaystyle 24 + 48 = 72$

The answer is 72. $\displaystyle 72.$

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Example Question #291 : How To Find The Square Root

Simplify the following:

$\sqrt{64}$ $\displaystyle \sqrt{64}$

Possible Answers:

$\pm8$ $\displaystyle \pm8$

$\displaystyle 64$

$\displaystyle 7$

$\displaystyle 28$

$\displaystyle 32$

Correct answer:

$\pm8$ $\displaystyle \pm8$

Explanation:

To simplify $\sqrt{64}$ $\displaystyle \sqrt{64}$, we will look at the definition of square roots.

$\sqrt{64} = \square$ $\displaystyle \sqrt{64} = \square$

$\square^2 = 64$ $\displaystyle \square^2 = 64$

We know the square root of a number is the same as taking that number and squaring it.

So, what number do we square to get 64?

The answer is 8.

$\sqrt{64} = \pm8$ $\displaystyle \sqrt{64} = \pm8$

$(\pm8)^2 = 64$ $\displaystyle (\pm8)^2 = 64$

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Example Question #291 : Isee Middle Level (Grades 7 8) Mathematics Achievement

$\sqrt{0.49}$ $\displaystyle \sqrt{0.49}$

Possible Answers:

0.007 $\displaystyle 0.007$

$\displaystyle 7$

0.7 $\displaystyle 0.7$

0.00007 $\displaystyle 0.00007$

Correct answer:

0.7 $\displaystyle 0.7$

Explanation:

$\sqrt{0.49} = 0.7$ $\displaystyle \sqrt{0.49} = 0.7$

Because $0.7 \times 0.7 - 0.49$ $\displaystyle 0.7 \times 0.7 - 0.49$

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Example Question #294 : How To Find The Square Root

Solve:

$x^{2} =\frac{64}{144}$ $\displaystyle x^{2} =\frac{64}{144}$

Possible Answers:

$x = \pm \frac{2}{3}$ $\displaystyle x = \pm \frac{2}{3}$

$\pm12$ $\displaystyle \pm12$

$x = \pm \frac{3}{2}$ $\displaystyle x = \pm \frac{3}{2}$

$\pm8$ $\displaystyle \pm8$

Correct answer:

$x = \pm \frac{2}{3}$ $\displaystyle x = \pm \frac{2}{3}$

Explanation:

$x^{2} =\frac{64}{144}$ $\displaystyle x^{2} =\frac{64}{144}$

Take the square root of each side

$\sqrt{x^{2}} = \frac{\sqrt{64}}{\sqrt{144}} or - \frac{\sqrt{64}}{\sqrt{144}}$ $\displaystyle \sqrt{x^{2}} = \frac{\sqrt{64}}{\sqrt{144}} or - \frac{\sqrt{64}}{\sqrt{144}}$

$x = \frac{8}{12} or -\frac{8}{12}$ $\displaystyle x = \frac{8}{12} or -\frac{8}{12}$

Reduce to simplest form

$x = \pm \frac{2}{3}$ $\displaystyle x = \pm \frac{2}{3}$

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Example Question #292 : How To Find The Square Root

Estimate $\sqrt{82}$ $\displaystyle \sqrt{82}$ to the nearest whole number.

Possible Answers:

$\displaystyle 8$

$\displaystyle 10$

$\displaystyle 9$

$\displaystyle 11$

Correct answer:

$\displaystyle 9$

Explanation:

The first perfect square less than 82 is 81.

The first perfect square greater than 82 is 100.

$\sqrt{81} < \sqrt{82} < \sqrt{100}$ $\displaystyle \sqrt{81} < \sqrt{82} < \sqrt{100}$

$9< \sqrt{82} < 10$ $\displaystyle 9< \sqrt{82} < 10$

$\sqrt{82}$ $\displaystyle \sqrt{82}$ is between $\displaystyle 9$ and 10. $\displaystyle 10.$

Since $\displaystyle 82$ is closer to $\displaystyle 81$ than to 100, $\displaystyle 100,$ the best whole number estimate for

$\sqrt{82}$ $\displaystyle \sqrt{82}$ is $\displaystyle 9.$

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Example Question #293 : How To Find The Square Root

Estimate to the nearest whole number.

$\sqrt{14.3}$ $\displaystyle \sqrt{14.3}$

Possible Answers:

$\displaystyle 4$

$\displaystyle 3$

$\displaystyle 5$

$\displaystyle 6$

Correct answer:

$\displaystyle 4$

Explanation:

$\sqrt{14.3}$ $\displaystyle \sqrt{14.3}$

The first perfect square less than 14.3 $\displaystyle 14.3$ is $\displaystyle 9$.

The first perfect square greater than 14.3 $\displaystyle 14.3$ is 16. $\displaystyle 16.$

$\sqrt{9}< \sqrt{14.3} < \sqrt{16}$ $\displaystyle \sqrt{9}< \sqrt{14.3} < \sqrt{16}$

$3< \sqrt{14.3} < 4$ $\displaystyle 3< \sqrt{14.3} < 4$

Therefore the $\sqrt{14.3}$ $\displaystyle \sqrt{14.3}$ lies between $\displaystyle 3$ and $\displaystyle 4.$

Because 14.3 is closer to 16, the best whole number estimate for $\sqrt{14.3}$ $\displaystyle \sqrt{14.3}$ is $\displaystyle 4.$

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Example Question #292 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Solve by finding the square root:

$\sqrt{49}*7$ $\displaystyle \sqrt{49}*7$

Possible Answers:

$\displaystyle 0$

$\displaystyle 14$

$\displaystyle 56$

$\displaystyle 49$

Correct answer:

$\displaystyle 49$

Explanation:

First, find the square root:

$\sqrt{49}=7$ $\displaystyle \sqrt{49}=7$

Then, solve:

7*7=49 $\displaystyle 7*7=49$

Answer: $\displaystyle 49$

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Example Question #293 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Solve by finding the square roots:

$\sqrt{64}\div \sqrt{16}$ $\displaystyle \sqrt{64}\div \sqrt{16}$

Possible Answers:

$\displaystyle 32$

$\displaystyle 4$

$\displaystyle 12$

$\displaystyle 2$

Correct answer:

$\displaystyle 2$

Explanation:

First, the square roots:

$\sqrt{64}=8$ $\displaystyle \sqrt{64}=8$

$\sqrt{16}=4$ $\displaystyle \sqrt{16}=4$

Then solve:

$8\div 4=2$ $\displaystyle 8\div 4=2$

Answer: $\displaystyle 2$

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Example Question #294 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Solve:

$\sqrt{121}*\sqrt{49}=$ $\displaystyle \sqrt{121}*\sqrt{49}=$

Possible Answers:

$\displaystyle 52$

170 $\displaystyle 170$

$\displaystyle 77$

$\displaystyle 7$

Correct answer:

$\displaystyle 77$

Explanation:

To solve, first find the square root:

$\sqrt{121}=11$ $\displaystyle \sqrt{121}=11$

$\sqrt{49}=7$ $\displaystyle \sqrt{49}=7$

Then, solve: 11*7=77 $\displaystyle 11*7=77$

Answer: $\displaystyle 77$

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Example Question #295 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Solve: $\sqrt{25}*\sqrt{169}=$ $\displaystyle \sqrt{25}*\sqrt{169}=$

Possible Answers:

$\displaystyle 8$

$\displaystyle 65$

$\displaystyle 18$

224 $\displaystyle 224$

Correct answer:

$\displaystyle 65$

Explanation:

To solve, first find the square root:

$\sqrt{25}=5$ $\displaystyle \sqrt{25}=5$

$\sqrt{169}=13$ $\displaystyle \sqrt{169}=13$

Then, solve: 5*13=65 $\displaystyle 5*13=65$

Answer: $\displaystyle 65$

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : ISEE Middle Level (grades 7-8) Mathematics Achievement

Study concepts, example questions & explanations for ISEE Middle Level Math

All ISEE Middle Level Math Resources

Example Questions

Example Question #291 : How To Find The Square Root

Example Question #291 : How To Find The Square Root

Example Question #291 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #294 : How To Find The Square Root

Example Question #292 : How To Find The Square Root

Example Question #293 : How To Find The Square Root

Example Question #292 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #293 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #294 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #295 : Isee Middle Level (Grades 7 8) Mathematics Achievement

All ISEE Middle Level Math Resources

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