Find Your Roots

$\color{#D61F06}{\sqrt{\frac{1}{\sqrt{x}}}=3\\ \frac{1}{\sqrt{x}}=9\\ \sqrt{x}=\frac{1}{9}\\x=\boxed{\frac{1}{81}}}$

$\sqrt {\frac {1}{\sqrt {x}}} = 3$

First you square both sides to get rid of one of the square roots

$\sqrt {\frac {1}{\sqrt {x}}} = 3 \Rightarrow \frac {1}{\sqrt {x}} = 9$

Since $\sqrt {1} = 1$ we can re-write it as

$\sqrt {\frac {1}{x}} = 9$

Squaring again gives us

$\frac {1}{x} = 81$

Multiply both sides by $x$ to get rid of the $x$ on the bottom

$1 = 81x$

Divide by $81$

$x = \frac {1}{81}$

So the answer is $\frac {1}{81}$

My method took a little bit longer than a few other methods, but it is the first method that came to mind.

$\sqrt{\frac{1}{\sqrt{x}}} = 3$

${\frac{1}{\sqrt{x}}} = 9$

${\frac{\sqrt{x}}{x}} = {\frac{9\sqrt{x}}{\sqrt{x}}}$

$\sqrt{x} = {\frac{9x\sqrt{x}}{\sqrt{x}}}$

$\sqrt{x} = 9x$

$x = 81x^{2}$

$1 = 81x$

$x = 1/81$

A man lives at tenth floor of a block of flats he can reach to number 8 BUT hes lucky thats its raining how is it possible

√[1/(√x )] = 3

√{1/[x^(1/2)]} = 3

√[x^(-1/2)] = 3

[x^(-1/2)]^(1/2) = 3

x^(-1/4) = 3

[x^(-1/4)]^-4 = 3^-4

x^(-4/-4) = 1/(3^4)

x = 1/81

here it is:

             √ (1/√x) =3

or, {√ (1/√x)}^2 = 3^2 ......................................[whole square]

or, 1/√x = 9

or, √x= 1/9

or, (√x)^2= (1/9)^2

or, x= 1/81

Tbh I just guessed...

$\sqrt{\frac{1}{\sqrt{x}}}=3 \implies \frac{1}{\sqrt{x}}=9 \implies \sqrt{x}=\frac{1}{9} \implies x=\boxed{\large{\frac{1}{81}}}$

square both sides, square both sides again ... x = 1/81

As we have two square root signs in LHS we have to remove one of it to make equation simpler. So first we will square it. i.e 1/√x=9 Now as we want the value of x we will square it again. i.e 1/x=81 i.e X=1/81

Substitute $x$ for $\frac{1}{81}$ and look at this method. Remember $1$ over $\frac{1}{81}$ basically means $\frac{81}{1}$ which leads us into having $81$ . So the root of $81$ is $9$ and the root of $9$ is 3 .

√(1/√x) = 3

(1/√x) = 9

√x/x = 9

√x = 9x

x = 81x²

x/x² = 81x²/x²

x-¹ = 81

1/x = 81

1 = 81x

1/81 = x

That took longer than it should.

Square both sides to remove d square root on d LHS {√1/√x}^2=3^2....1/√x=9.....√x=1/9....x=1/81

Errr..... Why is the answer is in bold?