Question

$\sqrt{2\sqrt{4\sqrt{5\sqrt{9\sqrt{x-2} } } } } = 16$

Find the value of x.

Answer 1

$\sqrt{2\sqrt{4\sqrt{5\sqrt{9\sqrt{x-2} } } } } = 16$

we known that

sqrt 4 = 2 and -2

sqrt9 = 3 and -3

Now

$\sqrt{4 \sqrt{15 \sqrt{x - 2} } } = 16$

again

$2 \sqrt{15 \sqrt{x - 4} } = 16$

on dividing both side by 2 we get

$\sqrt{15 \sqrt{x - 4} } = 8$

on sqiring both side we get

$15 \sqrt{x - 4} = 64$

again on sqiring we get

$x - 4 = \frac{ {64}^{2} }{225}$

$x = \frac{4096}{225} + 4$

so

$x = \frac{4096 + 900}{225}$

$x = \frac{4996}{225}$

Answer 2

$\sqrt{2\sqrt{4\sqrt{5\sqrt{9\sqrt{x-2} } } } } = 16$

$\sqrt{ 4\sqrt{ 15\sqrt{x - 2} } } = 16$

$2 \sqrt{15 \sqrt{ x - 4} } = 16$

$Divide \: Both \: Side \: by \: 2$

$\sqrt{ 15\sqrt{x - 4} } =8$

$Squaring \: both \: sides$

$15 \sqrt{x - 4} = 64$

$Again \: \: Squaring$

$\: \: \: \: x - 4 = \frac{ {(64)}^{2} }{225} \\ \\ \: \: \: \: x = \frac{4 ,096}{225} + 4 \\ \\ \: \: \: \: \: \: \: \: \: x = \frac{4 ,096 + 900}{225} \\ \\ \ \: \: \: \ x = \frac{4 ,996}{225}$