Evaluate the following:
(i) $ \left[\left(5^{2}+12^{2}\right)^{\frac{1}{2}}\right]^{3} $
(ii) $ \left[\left(6^{2}+8^{2}\right)^{\frac{1}{2}}\right]^{3} $.

To do:

We have to evaluate the given expressions.

Solution:

(i) $[(5^{2}+12^{2})^{\frac{1}{2}}]^{3}=[(25+144)^{\frac{1}{2}}]^{3}$

$=[(169)^{\frac{1}{2}}]^{3}$

$=[(13^{2})^{\frac{1}{2}}]^{3}$

$=(13)^{2 \times \frac{1}{2} \times 3}$

$=13^{3}$

$=2197$

(ii) $[(6^{2}+8^{2})^{\frac{1}{2}}]^{3}=[(36+64)^{\frac{1}{2}}]^{3}$

$=[(100)^{\frac{1}{2}}]^{3}$

$=[(10^{2})^{\frac{1}{2}}]^{3}$

$=(10)^{2 \times \frac{1}{2} \times 3}$

$=10^{3}$

$=1000$

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Updated on: 10-Oct-2022

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