Question

simplify root 2 + 1 / root 5​

Answer 1

Answer:

√2 + 1/√5

(√2+1)√5/√5(√5)

√5(√2+1)/5 -----eq(1)

√10 + √5/5

put the value of √5 &√2 in eq (1)

2.23(1.41+1)/5

2.23(2.41)/5

5.37/5

1.074

Answer 2

Root 2 + 1 / root 5​ can be simplified as $\frac{5\sqrt{2}+\sqrt{5}}{5}$.

Step-by-step explanation:

According to the given information the problem to simplify is,

root 2 + 1/root 5.

Now, root 2 + 1/root 5

= $\sqrt{2} +\frac{1}{\sqrt{5} }$

Taking least common multiple of the denominator, we get,

$\frac{\sqrt{2} \sqrt{5}+1 }{\sqrt{5} } \\=\frac{\sqrt{10}+1 }{\sqrt{5}}$

Multiplying both the numerator and the denominator by $\sqrt{5}$ for further simplification, we get,

$\frac{\sqrt{5}\sqrt{10} +\sqrt{5} }{\sqrt{5}*\sqrt{5} }$

This is equal to,

$\frac{\sqrt{5}\sqrt{5*2} +\sqrt{5} }{5} }\\\\=\frac{5\sqrt{2}+\sqrt{5}}{5}$

Therefore, root 2 + 1 / root 5​ can be simplified as $\frac{5\sqrt{2}+\sqrt{5}}{5}$.

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