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# Square root of decimal

Learn how to find the square root of a decimal number. The problem solved in this video is p^2 = 0.81.

## Want to join the conversation?

• What if the decimal doesn't go in as easily as .9 to .81? •   Use a calculator, but if you can't you could do this:
p^2=0.50
p=√0.50
p=√0.50
p=√0.25 *√2
p=0.5*√2
p=1/2 *√2
p=√2/2
It's just a simple example, but it works, and it can help you with some of the more complicated problems.
If you're wondering about the problems like the square root of 0.15, well, those cant be simplified because they don't have square roots inside of them (if you don't believe me, look it up or check your calculator)
If you did not notice, √0.50 has 0.25, which is a square root (0.5^2 = 0.25, √0.25=0.5). So if you do this and can't find the square roots inside of the root you're solving for, that just means it can't be simplified or solved for, so don't panic. Just look for square roots inside the root you're solving for, and if you don't find any, that means it can't be simplified.
If you want to go further:
First, you would find the √2:
You can use the Estimation and Approximation Method:
y=√x
((x/y)+y)/2
y_n+1 = ((x/y_n) + y_n)/2
y1 = (2 + 1)/2 = 1.5
y2 = (4/3 + 3/2)/2 = 1.4166
y3 = (24/17 + 17/12)/2 = 1.414215...
So, then you would divide that by two (I will be going to the thousands place)~
1.414/2 =(aproximatly) 0.707
(In the comments there is a link to the website I used for this, it won't allow me to put it in)
~ Woohoo
• Isn't -0.9 squared equal to -0.81. Technically, (-0.9) squared is the answer. Use the calculator. I think I am right. Am I? • at why does he put the plus or minus sign? •  When we multiply +9 x +9 we get 81 also when we multiply -9 x -9 we still get 81. so the square root can be + or - 9. therefore he writes + and - as the root can be either in + or -.
• What if the number was a fraction? Would I try to just simplify it down to shortest terms possible in decimal form and work from there? I have a problem of finding the square root of 49/81. • what about number like the square root of 1.69 or 4.84? •  Find the square root of 169 (no decimal points). It = 13.
Then figure out how many decimal points you need in your answer. 1.3 x1.3 = 1.69.
So, sqrt(1.69) = 1.3

Alternatively, do them as fractions. 1.69 = 169/100
sqrt(169/100) = sqrt(169) / sqrt(100) = 13/10 = 1.3
• At Sal counts the number of decimal points in the expression, in order to find the number of decimal points in the answer. I've seen this been done before, and I'm familiar with using the technique, but I'm wondering why it works. I've simply taken my teachers word and simply assumed it works because my teacher said so. But now I'm actually curious, why does this technique, for finding the number of decimal places in the answer, work? • how to calculate the cube root of decimal numbers? • In the "into to cube roots" video Sal showed how doing the prime factorization of a number can help you figure out its cube root. Take 64 which can break down into 4x16; 16 breaks down into 4x4; so if you multiply 4x4x4 you get 64. Take 0.125 which can break down into .5x.25; .25 breaks down into .5x.5; so if you multiply .5x.5x.5 you get .125
• Is any number squared always a positive number?   