Question

simplify it and Answer ​

Answer 1

Answer:

$\frac{ \sqrt{18} }{5 \sqrt{18} + 3 \sqrt{72} + 2 \sqrt{162} }$

$\frac{ \sqrt{18} }{5 \sqrt{18} + 3 \sqrt{4 \times 18} + 2 \sqrt{9 \times 18} }$

$\frac{ \sqrt{18} }{5 \sqrt{18} + 3 \times 2 \sqrt{18} + 2 \times 3 \sqrt{18} }$

$\sqrt{4} = 2 \: \: and \: \: \sqrt{9} = 3$

$\frac{ \sqrt{18} }{5 \sqrt{18} + 6 \sqrt{18} + 6 \sqrt{18} }$

$\frac{ \sqrt{18} }{17 \sqrt{18} }$

$\frac{1}{17}$

Answer 2

Required Answer:-

Here we have some complex surds. First of all, simplify the surds into the simplest form. Refee to the attachment.

We got,

• √18 = 3√2
• √72 = 6√2
• √162 = 9√2

Simplifying the above question,

$\large{= \frac{ \sqrt{18} }{5 \sqrt{18} + 3 \sqrt{72} + 2 \sqrt{162} }}$

$\large{ = \frac{3 \sqrt{2} }{5 \times 3 \sqrt{2} + 3 \times 6 \sqrt{2} + 2 \times 9 \sqrt{2} }}$

$\large{= \frac{3 \sqrt{2} }{15 \sqrt{2} + 18 \sqrt{2} + 18 \sqrt{2} }}$

$\large{= \frac{3 \sqrt{2} }{51\sqrt{2} } }$

$\large{= \frac{1}{17} ( \tt{ans})}$

And the simplified form is 1/17