Question

$\sf \red{ \frac{Solve \: this}{━━━━━━━━━━━━━━━}}$
$\sf {if \: \sqrt{x^{2} - 36 } = 8}$
$\sf {Find \: x}$
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Answer 1

Answer:

Analysis→

Here we're given a condition that $\rm\sqrt{x^2-36}=8$ And we've to the value of x which satisfies the equation. But as there is an over root in the equation, so first we've to open the root to ease the calculation.

Given→

• Equation= $\rm\sqrt{x^2-36}=8$

To Find→

The value of x.

Answer→

$\implies\rm{\sqrt{x^2-36}=8}$

$\implies\rm{\big(\sqrt{x^2-36}\big)^2=\big(8\big)^2}$

$\implies\rm{x^2-36=64}$

$\implies\rm{x^2=100}$

$\implies\rm{x=\sqrt{100}}$

$\implies\rm{x=10}$

${\boxed{\boxed{\implies{\bf{x=10\checkmark}}}}}$

☆Verification

$\implies\rm{ \sqrt{x^2-36}=8}$

$\implies\rm{ \sqrt{(10)^2-36}=8}$

$\implies\rm{ \sqrt{100-36}=8}$

$\implies\rm{ \sqrt{64}=8}$

$\implies\bf{8=8}$

${\underline{\underline{\bf{Hence\:Verified\checkmark}}}}$

☞Hence the value of x is 10 which is the required answer.

HOPE IT HELPS.

Answer 2

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$\sqrt {x ^{2} - 36} = 8 \\ {x}^{2} - 36 = {8}^{2} \\ {x}^{2} - 36 = 64 \\ {x}^{2} = 64 + 36 \\ {x}^{2} = 100 \\ x = \sqrt{100} \\ x = 10$

$\pink {hope \: it \: helps \: u}$

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