Question

it being given that √3=1.732,√5=2.236,√6=2.449 and √10=3.162, find to three places of decimal, the value of each of the following.

1
√6+√5

Answer 1

As √6=2.449 & √5=2.236
So,√6+√5=2.449+2.236=4.685
But, you are asking to find up to three places and 4.685 is up to 3 places after the decimal..
So,4.685 will be the correct answer.
Hope, you will like it.

Answer 2

Answer:

Value of $\frac{1}{\sqrt{6}+\sqrt{5}}\:is\:0.213$

Step-by-step explanation:

Given: Value of √3 = 1.732 , √5 = 2.236 , √6 = 2.449 and √10 = 3.162

To find: value of $\frac{1}{\sqrt{6}+\sqrt{5}}$

Consider,

$\frac{1}{\sqrt{6}+\sqrt{5}}$

$=\frac{1}{\sqrt{6}+\sqrt{5}}\times\frac{\sqrt{6}-\sqrt{5}}{\sqrt{6}-\sqrt{5}}$

$=\frac{\sqrt{6}-\sqrt{5}}{(\sqrt{6}-\sqrt{5})(\sqrt{6}+\sqrt{5})}$

$=\frac{\sqrt{6}-\sqrt{5}}{(\sqrt{6})^2-(\sqrt{5})^2}$

$=\frac{\sqrt{6}-\sqrt{5}}{6-5}$

$=\sqrt{6}-\sqrt{5}$

= 2.449 - 2.236

= 0.213

Therefore, Value of $\frac{1}{\sqrt{6}+\sqrt{5}}\:is\:0.213$