Question

Simplify 15 root 6 -root 216+ root 96​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

$15 \sqrt{6} -\sqrt{216} + \sqrt{96}$  =13√6

Step-by-step explanation:

Required to simplify

$15 \sqrt{6} -\sqrt{216} + \sqrt{96}$

Solution:

Prime factorization of 216 = 2×2×2×3×3×3

= 2²×3²×2×3

= 6²×6

$\sqrt{216}$ = $\sqrt{6^2X6}$ = 6√6

∴$\sqrt{216}$ =  6√6

Prime factorization of 96 = 2×2×2×2×2×3

=  2²×2²×2×3

= 4²×6

$\sqrt{96} =$ $\sqrt{4^2 X6}$ = 4√6

∴$\sqrt{96} =$4√6

Substituting the values of $\sqrt{216}$ and $\sqrt{96}$ we get

$15 \sqrt{6} -\sqrt{216} + \sqrt{96}$  =  15√6 - 6√6 + 4√6

=13√6

∴ $15 \sqrt{6} -\sqrt{216} + \sqrt{96}$  =13√6

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