Question

If √2 =1.414,√5=2.236 and√3=1.732, find the value of : 1. √72+√48 2. √125/64

Answer 1

Answer:

1. √72+√48

=6√2+4√3

=6×1.414+4×1.732

=8.484+6.928

=15.412

2. √125/64

=(5√5)/8

=11.18/8

=1.3975

Answer 2

Answer:

The values are 15.412 and 1.3975 respectively.

Step-by-step explanation:

a. To find: $\begin{aligned} \sqrt{72}+\sqrt{48} &=\sqrt{36 \times 2}+\sqrt{16 \times 3} \\ &=\sqrt{6 \times 6 \times 2}+\sqrt{4 \times 4 \times 3} \end{aligned}$

Since $\sqrt{a \times a}=a$

$\sqrt{6 \times 6 \times 2}+\sqrt{4 \times 4 \times 3}=6 \sqrt{2}+4 \sqrt{3}$

Given $\sqrt{2}=1.414, \sqrt{3}=1.732$

$6 \sqrt{2}+4 \sqrt{3}=6 \times 1.414+4 \times 1.732 =8.484+6.928 6 \sqrt{2}+4 \sqrt{3}=\bold{15.412 }$

b. To find: $\sqrt{\frac{125}{64}}=\sqrt{\frac{5+5+5}{8+8}}$

Since $\sqrt{a \times a}=a$

$\sqrt{\frac{125}{64}}=\frac{5}{8} \sqrt{5} =0.625 \sqrt{5} Given \sqrt{5}=2.236 =0.625 \times 2.236 \sqrt{\frac{125}{64}}=\bold{1.3975}$