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GED Math : Complex Operations

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Example Questions

Example Question #191 : Complex Operations

Simplify:

$\frac{(x^2y^3)^3z^5}{xyz}$

Possible Answers:

$\frac{x^3y^2}{z^4}$

$x^7y^{10}z^6$

$\frac{x^6y^5}{z}$

x^5y^8z^4

Correct answer:

x^5y^8z^4

Explanation:

Recall your exponent rules and order of operations. Start by simplifying the parenthetical term.

$\frac{(x^2y^3)^3z^5}{xyz}=\frac{x^6y^9z^5}{xyz}$

Recall that when you have terms with the same base but different exponents being divided, you will need to subtract the exponent found in the denominator from the exponent found in the numerator.

$\frac{x^6y^9z^5}{xyz}=x^5y^8z^4$

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Example Question #192 : Complex Operations

Simplify the following expression:

$\frac{6x^4y^9b^{12}}{15x^3y^9b^8}$

Possible Answers:

$\frac{2}{5}xb^4$

Undefined.

Correct answer:

$\frac{2}{5}xb^4$

Explanation:

Simplify the following expression:

$\frac{6x^4y^9b^{12}}{15x^3y^9b^8}$

To simplify this expression, we need to cancel out our common terms. In order to do so, we need to subtract the exponents, and treat the coefficients (whole numbers) like a regular fraction.

So, we can rewrite our expression as follows:

$\frac{6}{15}(x^{4-3}y^{9-9}b^{12-8})=\frac{2}{5}x^1y^0b^4$

Now, we can simplify this further by dropping the exponent on the x (an exponent of 1 is the same as the variable by itself). And by dropping the y entirely (an exponent of 0 means that the term is just 1).

So, we get:

$\frac{2}{5}x^1y^0b^4=\frac{2}{5}xb^4$

$\frac{2}{5}xb^4$

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Example Question #193 : Complex Operations

Simplify

$\frac{(x^2)^5}{(x^{\frac{1}{2}})^4}$

Possible Answers:

$\frac{x^{10}}{x^2}$

x^5

$x^{10}$

x^8

It is already simpified

Correct answer:

x^8

Explanation:

Recall that when you have a power to a power, you can simplify by multiplying the powers. Let's use that to simplify the numerator and the denominator.

$\frac{(x^2)^5}{(x^{\frac{1}{2}})^4}=\frac{x^{2\cdot 5}}{x^{\frac{1}{2}\cdot 4}}=\frac{x^{10}}{x^2}$

Now recall that when you have two powers with the SAME base in the numerator and denominator, you can simplify by subtracting the exponents.

$\frac{x^{10}}{x^2}=x^{10-2}=x^8$

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Example Question #194 : Complex Operations

Simplify:
$\small \sqrt{192}$

Possible Answers:

$\small 16\sqrt{12}$

$\small 64\sqrt3$

$\small 4\sqrt{12}$

$\small \small 8\sqrt3$

Correct answer:

$\small \small 8\sqrt3$

Explanation:

$\small \sqrt{192}=\sqrt{64}\times \sqrt3=8\times \sqrt3=8\sqrt3$

An alternate solution is:

$\small \sqrt{192}=\sqrt{16}\times \sqrt{12}=4\times \sqrt{4} \times \sqrt3=4\times2\times\sqrt3=8\sqrt3$

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Example Question #2 : Square Roots And Radicals

Simplify:

$\small \sqrt{x^4}$

Possible Answers:

$\small x^3$

$\small \sqrt{x^4}$

$\small x^2$

$\small x$

Correct answer:

$\small x^2$

Explanation:

$\small \sqrt{x^4}=\sqrt{x^2}\times \sqrt{x^2}=x\times x=x^2$

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Example Question #195 : Complex Operations

Simplify:

$\small \sqrt{98}$

Possible Answers:

$\small 4\sqrt7$

$\small 49\sqrt2$

$\small 2\sqrt7$

$\small 7\sqrt2$

Correct answer:

$\small 7\sqrt2$

Explanation:

$\small \sqrt{98}=\sqrt{49}\times \sqrt{2}=7\times \sqrt2=7\sqrt2$

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Example Question #4 : Square Roots And Radicals

Simplify:

$\small \sqrt{72}=$

Possible Answers:

$\small 6\sqrt2$

$\small 2\sqrt6$

$\small 4\sqrt6$

$\small 36\sqrt2$

Correct answer:

$\small 6\sqrt2$

Explanation:

$\small \sqrt{72}=\sqrt{36}\times \sqrt2=6\times \sqrt2=6\sqrt2$

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Example Question #2 : Square Roots And Radicals

Simplify:

$\sqrt{147}$

Possible Answers:

$9\sqrt7$

$7\sqrt3$

$3\sqrt7$

$49\sqrt3$

Correct answer:

$7\sqrt3$

Explanation:

$\sqrt{147}=\sqrt{49}\times \sqrt3=7\times \sqrt3=7\sqrt3$

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Example Question #6 : Square Roots And Radicals

Numberline_1

Refer to the above number line. What point most likely represents the square root of 280?

Do not use a calculator.

Possible Answers:

Correct answer:

Explanation:

$16^{2} = 256 < 280 < 289 < 17^{2}$

Therefore, $16 < \sqrt{280} < 17$ ,

making the correct choice .

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Example Question #196 : Complex Operations

Simplify:

$\sqrt{48}$

Do not use a calculator.

Possible Answers:

The expression is in simplest form.

$6\sqrt{2}$

$3 \sqrt{6}$

$4\sqrt{3}$

Correct answer:

$4\sqrt{3}$

Explanation:

The prime factorization of 48 is

$48 = 2 \times 2 \times 2 \times 2 \times 3$ .

Rewrite, and use the product of radicals property to simplify:

$\sqrt{48}$

$= \sqrt{ 2 \times 2 \times 2 \times 2 \times 3}$

$= \sqrt{ 2 \times 2 } \times \sqrt{ 2 \times 2 } \times \sqrt{ 3}$

$= 2 \times 2 \times \sqrt{ 3}$

$=4 \sqrt{ 3}$

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GED Math : Complex Operations

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #191 : Complex Operations

Example Question #192 : Complex Operations

Example Question #193 : Complex Operations

Example Question #194 : Complex Operations

Example Question #2 : Square Roots And Radicals

Example Question #195 : Complex Operations

Example Question #4 : Square Roots And Radicals

Example Question #2 : Square Roots And Radicals

Example Question #6 : Square Roots And Radicals

Example Question #196 : Complex Operations

All GED Math Resources

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