Question 132574
12 * 12 = 144

13 * 13 = 169


{{{144 < 150 < 169}}}, so {{{12 < sqrt(150) < 13}}}


{{{150 - 144 = 6}}} and {{{169 - 144 = 25}}}, so {{{sqrt(150)}}} is close to {{{6/25}}} of the way from 12 to 13.


{{{6/25=.24}}}, so {{{sqrt(150)}}} is very close to 12.24.


{{{12.2^2=148.84}}}, {{{150 - 148.84 = 1.16}}}
{{{12.3^2=151.29}}}, {{{151.29 - 150 = 1.29}}}


Now we know that {{{12.2 < sqrt(150) < 12.3}}} and that 12.2 is closer to {{{sqrt(150)}}} than 12.3, so 12.2 is the square root of 150 to the nearest 10th.


Easier way:
Press 1, 5, 0, and the square root key on your calculator.  Round the answer to the nearest tenth.