Question

find the value of [(5^2+12^2)^1/2]^3

Answer 1

[(5^2+12^2)^1/2]^3

=[(25+144)^1/2]^3

=[169^1/2]^3

=13^3

=2197

Answer 2

$\bold{( ({{5}^{2} + {12}^{2} })^{ \frac{1}{2} } ) {}^{3}}$


First, solving the content which is in the brackets.

( 5² + 12² )
= > ( 25 + 144 )
= > 169



$\bold{((169) {}^{\frac{1}{2} } {)}^{ 3}}$



Now, Factorizing 169. On Factorizing 169 we get 13 × 13 which can be also written as 13². So writing 13² in place of 169



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



From the properties of exponents, ( a² )ⁿ = a²ⁿ



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


Cancel out 2.



$\bold{ {13}^{3} }$


13³ can be also written as 13 × 13 × 13 or 169 × 13


So, it will be


$= \bold{13 \times 13 \times 13} \\ \\ = > \bold{ 169 \times 13} \\ \\ = > \bold{2197}$