Knight Colon
05/24/2024 · Junior High School
(8) Simplify: \( \sqrt{45 x y^{3} z^{2}} \)
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Tutor-Verified Answer
Step-by-step Solution
Calculate or simplify the expression \( \sqrt(45*x*y^3*z^2) \).
Simplify the expression by following steps:
- step0: Solution:
\(\sqrt{45xy^{3}z^{2}}\)
- step1: Write as a product:
\(\sqrt{9\times 5xy^{3}z^{2}}\)
- step2: Write in exponential form:
\(\sqrt{3^{2}\times 5xy^{3}z^{2}}\)
- step3: Rewrite the exponent:
\(\sqrt{3^{2}\times 5xy^{2+1}z^{2}}\)
- step4: Expand the expression:
\(\sqrt{3^{2}\times 5xy^{2}\times yz^{2}}\)
- step5: Reorder the terms:
\(\sqrt{3^{2}y^{2}z^{2}\times 5xy}\)
- step6: Use the properties of radicals:
\(\sqrt{3^{2}y^{2}z^{2}}\times \sqrt{5xy}\)
- step7: Simplify the root:
\(3yz\sqrt{5xy}\)
The simplified form of \( \sqrt{45 x y^{3} z^{2}} \) is \( 3yz\sqrt{5xy} \).
Quick Answer
\( 3yz\sqrt{5xy} \)
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