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# Algebra

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121
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Calculate sqrt(60x)*sqrt(12x)*sqrt(63x)*sqrt(42x). Express your answer in simplest radical form in terms of x. Note: When entering a square root with more than one character, you must use parentheses or brackets. For example, you should enter sqrt(14) as "sqrt(14)" or "sqrt{14}".

Jan 29, 2022

#1
+2437
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https://web2.0calc.com/questions/algebra-question_120#r1. I answered the question here

Jan 29, 2022
#2
+1224
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$$\sqrt{60x} \cdot \sqrt{12x} \cdot \sqrt{63x} \cdot \sqrt{42x}$$

$$= \sqrt{60x \cdot 12x \cdot 63x \cdot 42x}$$

$$= \sqrt{(2^2 \cdot 3 \cdot 5) \cdot (2^2 \cdot 3) \cdot (3^2 \cdot 7) \cdot (2 \cdot 3 \cdot 7) \cdot x^4}$$

$$= \sqrt{2^5 \cdot 3^5 \cdot 5 \cdot 7^2 \cdot x^4}$$

$$= 2^2 \cdot 3^2 \cdot 7 \cdot x^2 \cdot \sqrt{2 \cdot 3 \cdot 5}$$

$$= \boxed{252x^2 \sqrt{30}}$$

tl;dr: split each number into their prime factors, multiply them all, then move the perfect squares outside the square root

Jan 29, 2022