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# Square Roots of Imperfect Squares

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## Michelle Ernst

on 9 September 2012

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#### Transcript of Square Roots of Imperfect Squares

Square Roots of Imperfect Squares First, let's review. When determining the square root,
you are looking for a number when multiplied by itself
number under the radical symbol. For example: These are called
perfect squares! Imperfect squares are a bit different. The square root of 10 is an imperfect square
because no whole number multiplies itself to
become 10. Here's an example: We can find the closest square by solving the
square root of the closest perfect squares. 2 x 2 = 4
3 x 3 = 9
4 x 4 = 16 Find the square root of a perfect square that is just lower and just higher of the imperfect square. Lower perfect square: The square root of 9 is 3.
Higher perfect square: The square root of 16 is 4. The square root of 10 is between 3 and 4 but closer to 3 because 10 is closer to 9 than 16. Square root of 9 = 3
Square root of 10 = ?
Square root of 16 = 4 That is A LOT of information!
But let's try another one using the steps we just learned. First, is it a perfect or imperfect square? Why? Let's try the square root of 33. Lower perfect square: 25
Higher perfect square: 36 What is a perfect square lower and higher than 33? Square root of 25 is 5.
Square root of 36 is 6. So, the square root of 33 is between 5 and 6. The square root of 25 = 5
The square root of 33 = ?
The square root of 36 = 6

The square root of 33 is closer to which number: 5 or 6? Why? The square root of 50. Here's another one: What is the first step? The closest lower perfect square is 49.
The closest higher perfect square is 64. The square root of 49 is 7.
The square root of 64 is 8. But, is it closer to 7 or 8?
Explain how you know? So, the square root of 50 is between 7 and 8. Square root of 49 = 7
Square root of 50 = ?
Square root of 64 = 8 What is the square root of 95? Finally, try this one on your own. Closest lower perfect square is 81.
Closest higher perfect square is 100. Square root of 81 = 9
Square root of 100 = 10

So, the square root of 95 is between
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