Get the answer to "To calculate The value of expression 40x5y63"

High School
Algebra
Pre-Algebra
Factors and multiples

generals336

Answered question

2021-08-07

To calculate The value of expression $\sqrt[3]{40 x^{5} y^{6}}$

Answer & Explanation

smallq9

Skilled2021-08-08Added 106 answers

Formula used:
For an n-th root, identify factors in the radicand with exponents that are multiples of n.
Calculation:
The expression $\sqrt[3]{40 x^{5} y^{6}}$ can be expanded by identifying the largest exponents and multiples of 3.
$\sqrt[3]{40 x^{5} y^{6}} = \sqrt[3]{8 \cdot 5 \cdot x^{3} \cdot x^{2} \cdot x^{6}}$
Now separate the largest perfect cube factors.
$\sqrt[3]{8 \cdot 5 \cdot x^{3} \cdot x^{2} \cdot x^{6}} = \sqrt[3]{8} \cdot \sqrt[3]{x^{3}} \cdot \sqrt[3]{y^{6}} \cdot \sqrt[3]{5 x^{2}}$
After simplifying it further,
$\sqrt[3]{8} \cdot \sqrt[3]{x^{3}} \cdot \sqrt[3]{y^{6}} \cdot \sqrt[3]{5 x^{2}} = 2 \cdot x \cdot y^{2} \sqrt[3]{5 x^{2}}$
$= 2 x y^{2} \sqrt[3]{5 x^{2}}$
Hence, the value of expression is $= 2 x y^{2} \sqrt[3]{5 x^{2}}$

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