Square Roots
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Algebra II › Square Roots
Evaluate the radical:
Explanation
In order to get the most simplified answer, do not multiply all the numbers together and combine as one radical.
Rewrite each radicals in their most simplified form.
Multiply the terms.
Notice that multiplying a square root of a number by itself will leave only the integer and will eliminate the radical.
The terms become:
The answer is:
Simplify:
Explanation
To simplify, we must find the squares that are underneath each radical (this can be easier to see after some factoring):
The squares are easier to identify now! We can pull them out of the radical after taking their square root, leaving behind everything that is not a square:
Evaluate:
Explanation
Evaluate each square root. The square root of a number evaluates into a number which multiplies by itself to achieve the number in the square root.
Substitute the terms back into the expression.
The answer is:
Evaluate:
Explanation
Evaluate each square root. The square root of the number is equal to a number multiplied by itself.
The answer is:
Simplify:
Explanation
Evaluate by solving each square root first. The square root of a number is a number that multiplies by itself to achieve the number inside the square root.
Rewrite the expression.
The answer is:
Solve:
Explanation
Solve each radical. The square root determines a number that multiples by itself to equal the number inside the square root.
Rewrite the expression.
The answer is:
Simplify by rationalizing the denominator:
Explanation
Multiply the numerator and the denominator by the conjugate of the denominator, which is . Then take advantage of the distributive properties and the difference of squares pattern:
Evaluate the square root:
Explanation
The coefficients of the terms share the same square root. This means that the terms can be combined as a single square root.
Add the coefficients.
The answer is:
Evaluate the product of square roots:
Explanation
We can rewrite the expression by using common factors.
The radical square root nine is a perfect square. The other two radicals can be multiplied together to form one radical.
The answer is:
Solve:
Explanation
Solve by evaluating the square roots first.
Substitute the terms back into the expression.
The answer is: