How do you find the square root of #100# ?

1 Answer
Jul 14, 2015

The (positive) square root of #100# is #10#.
#-10# is also a square root of #100#.

We write the positive square root of #100# as #sqrt(100)#

Explanation:

A square root of a number #n# is a number #x# such that #x^2 = n#.

As for how do you find the square root of #100#, you should encounter #100 = 10^2# often enough that it will become obvious.

#10^0 = 1#
#10^1 = 10#
#10^2 = 10 xx 10 = 100#
#10^3 = 10 xx 10 xx 10 = 1000#
etc.

So if you did not realise it already #10^2 = 10 xx 10 = 100#, so #10# is a solution to finding a number whose square is #100#.

In general, to find the square root of a larger number, it may be helpful to factor the number into prime numbers first.

For example:

#324 = 2*2*3*3*3*3 = 2^2*3^4#

Then we can split the powers of each prime evenly into two as follows:

#2^2*3^4 = (2^1*3^2)*(2^1*3^2) = 18*18 = 18^2#

If you prefer:

#2*2*3*3*3*3 = (2*3*3)*(2*3*3) = 18*18 = 18^2#

So #324 = 18^2# and #sqrt(324) = 18#

If it is not possible to split the prime factors into two identical groups in this way, then the square root is not a whole number. In fact it will not even be a rational number (improper fraction).

For example #27 = 3 * 3 * 3# cannot be expressed as #m^2# for some integer #m#, or even as #(p/q)^2# for some integers #p# and #q#.