Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

How do you find the square root of 137?

Answer
VerifiedVerified
470.1k+ views
1 likes
like imagedislike image
Hint:Here, we will solve this question by using a long division method to find the square root. We will pair each number except the first digit and divide it with a suitable number. We will find the square root correct to 1 decimal place and then we will write the required final value.

Complete step by step solution:
As we need to find the square root of the given number i.e. 137, so we will write 137 as 137.0000, as we take pairs of digits while calculating the square root.
In the long division method of finding the square root, we have to first find the square of a number which is closest to the first digit of a number i.e. 1.
We know that 12=1=1, therefore, we will divide 137 by 1 to obtain
11|137.000010
Thus, the first digit in 137 should be 1.
We have got the remainder as 0 and we will take down the next two digits after the decimal place. Now, the ones place of the divisor is of the form 1×2=2 and we will try to find out a number of the form 2x×x is lower than but closest to 37.
 As 21×1=21<37 therefore, we will divide 37 by 21 to obtain
121|372116
Thus, the second digit in 137 should be 1.
We have got the remainder as 16 and we will take down the next two digits after the decimal place. Now, the tens place of the divisor is of the form 20+1×2=22 and we will try to find out a number of the form 22x×x is lower than but closest to 1600
 As 227×7=1589<1600 therefore, we will divide 1600 by 227 to obtain
7227|1600158911
Thus, the first digit after the decimal point in 137 should be 7.

The square root of the number 137 is 11.7.

Note: A square root of a number is defined as the number which when multiplied by itself gives the original number. In other words, when we multiply that number twice, we will get the value that is equal to the given number. We can check if we have found the correct answer or not by multiplying the obtained square root twice.
11.7×11.7819117×117××136.89
After multiplying we get the numbers as 136.89 which is approximately 137.
Latest Vedantu courses for you
Grade 11 Science PCM | CBSE | SCHOOL | English
CBSE (2025-26)
calendar iconAcademic year 2025-26
language iconENGLISH
book iconUnlimited access till final school exam
tick
School Full course for CBSE students
PhysicsPhysics
ChemistryChemistry
MathsMaths
₹41,848 per year
Select and buy
WhatsApp Banner