Find the square root of each of the following correct to three places of decimal:
(i) 5
(ii) 7
(iii) 17
(iv) 20
(v) 66
(vi) 427
(vii) 1.7
(viii) 23.1
(ix) 2.5
(x) 237.615
(xi) 15.3215
(xii) 0.9
(xiii) 0.1
(xiv) 0.016
(xv) 0.00064
(xvi) 0.019
(xvii) $\frac{7}{8}$
(xviii) $\frac{5}{12}$
(xix) $2\frac{1}{2}$
(xx) $287\frac{5}{8}$

To do: 

We have to find the square roots of the given numbers correct to three places of decimal.

Solution:

(i) To find the square root to three places of decimal, we write 5 as,

$5=5.000000$

$\sqrt{5}=\sqrt{5.000000}$

Therefore,

$\sqrt{5}=2.236$  

(ii) To find the square root to three places of decimal, we write 7 as,

$7=7.00000000$

$\sqrt{7}=\sqrt{7.00000000}$

Therefore,

$\sqrt{7}=2.6457$

$=2.646$  

(iii) To find the square root to three places of decimal, we write 17 as,

$17=17.000000$

$\sqrt{17}=\sqrt{7.000000}$

Therefore,

$\sqrt{17}=4.123$ 

(iv) To find the square root to three places of decimal, we write 20 as,

$20=20.000000$

$\sqrt{20}=\sqrt{20.000000}$

Therefore,

$\sqrt{20}=4.472$  

(v) To find the square root to three places of decimal, we write 66 as,

$66=66.000000$

$\sqrt{66}=\sqrt{66.000000}$

Therefore,

$\sqrt{66}=8.124$  

(vi) To find the square root to three places of decimal, we write 427 as,

$427=427.00000000$

$\sqrt{427}=\sqrt{427.00000000}$

Therefore,

$\sqrt{427}=20.6639$ 

$=20.664$ 

(vii) To find the square root to three places of decimal, we write 1.7 as,

$1.7=1.70000000$

$\sqrt{1.7}=\sqrt{1.70000000}$

Therefore,

$\sqrt{1.7}=1.304$   

(viii) To find the square root to three places of decimal, we write 23.1 as,

$23.1=23.100000$

$\sqrt{23.1}=\sqrt{23.100000}$

Therefore,

$\sqrt{23.1}=4.806$ 

(ix) To find the square root to three places of decimal, we write 2.5 as,

$2.5=2.500000$

$\sqrt{2.5}=\sqrt{2.500000}$

Therefore,

$\sqrt{2.5}=1.581$  

(x) To find the square root to three places of decimal, we write 237.615 as,

$237.615=237.61500000$

$\sqrt{237.615}=\sqrt{237.615000000}$

Therefore,

$\sqrt{237.615}=15.415$  

(xi) To find the square root to three places of decimal, we write 15.3215 as,

$15.3215=15.321500$

$\sqrt{15.3215}=\sqrt{15.321500}$

Therefore,

$\sqrt{15.3215}=3.9142$

$=3.914$  

(xii) To find the square root to three places of decimal, we write 0.9 as,

$0.9=0.90000000$

$\sqrt{0.9}=\sqrt{0.90000000}$

Therefore,

$\sqrt{0.9}=0.9486$

$=0.949$  

(xiii) To find the square root to three places of decimal, we write 0.1 as,

$0.1=0.100000$

$\sqrt{0.1}=\sqrt{0.100000}$

Therefore,

$\sqrt{0.1}=0.316$

(xiv) To find the square root to three places of decimal, we write 0.016 as,

$0.016=0.01600000$

$\sqrt{0.016}=\sqrt{0.01600000}$

Therefore,

$\sqrt{0.016}=0.1264$

$=0.126$  

(xv) To find the square root to three places of decimal, we write 0.00064 as,

$0.00064=0.00064000$

$\sqrt{0.00064}=\sqrt{0.00064000}$

Therefore,

$\sqrt{0.00064}=0.0252$

$=0.025$  

(xvi) To find the square root to three places of decimal, we write 0.019 as,

$0.019=0.01900000$

$\sqrt{0.019}=\sqrt{0.01900000}$

Therefore,

$\sqrt{0.019}=0.138$

(xvii) $\frac{7}{8}=0.875$

To find the square root to three places of decimal, we write 0.875 as,

$0.875=0.87500000$

$\sqrt{0.875}=\sqrt{0.87500000}$

Therefore,

$\sqrt{\frac{7}{8}}=0.9354$

(xviii) $\frac{5}{12}=0.416666$

To find the square root to three places of decimal, we write 0.416666 as,

$0.416666=0.41666666$

$\sqrt{0.416666}=\sqrt{0.41666666}$

Therefore,

$\sqrt{\frac{5}{12}}=0.6454$

 $=0.645$

(xix) $2\frac{1}{2}=2.5$

To find the square root to three places of decimal, we write 2.5 as,

$2.5=2.500000$

$\sqrt{2.5}=\sqrt{2.500000}$

Therefore,

$\sqrt{2\frac{1}{2}}=1.581$

(xx) $287\frac{5}{8}=287.625$

To find the square root to three places of decimal, we write 287.625 as,

$287.625=287.625000$

$\sqrt{287.625}=\sqrt{287.625000}$

Therefore,

$\sqrt{287\frac{5}{8}}=16.959$

Tutorialspoint

Updated on: 10-Oct-2022

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