square roots and cube roots

square roots and cube roots

By DIANE WALLER

Square Roots

​What is a square root?

A square root is the inverse of "squaring" a number

​Squaring a number just means that a number is multiplied by itself ​TWO times, or said differently, a number to the power of TWO

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​s =5mm

​

​

​​​

A = s • s or ​ A = s²

This square has 5 mm sides​

​ We find the area of the square by

multiplying one side length times another side length

​Five squared is 5²

Why is it called squaring a number?

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A square has sides that are all the same length,​

Multiple Select

5 squared =

Choose all that are correct

• 5

• 10

• 25

• 5²

Multiple Choice

36

• 6¹

• 6²

• 3²

• 6³

Multiple Select

NINE SQUARED

• 9²

• 9³

• 18

• 81

Square Roots

​A root "undoes" a power

A square root is the inverse of a numbner to the 2nd power. FOr all othre powers, you must use a "root" for that number.

​

n⁵ has to be undone by a fifth root. Likewise n³ cube root to undo it.​

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SYMBOL FOR SQUARE ROOT

√

Multiple Choice

$$\sqrt[]{49}$$  

• 9

• 5

• 7

• 4

Multiple Choice

$$\sqrt[]{100}\ +\sqrt[]{16\ }\ =$$  

• 10

• 8

• 12

• 14

Multiple Select

$$\sqrt[3]{8\ }$$  

ALL OF THE ANSWERS BELOW ARE TRUE.

CHOOSE ALL FOUR

• Undoes when a number is raised to the 3rd power

  In this case 2³

• 2• 2 • 2

• IS READ "THE CUBE ROOT OF 8.

• MEANS what number is multiplied by itself THREE times to get this number.

Just find the square root of each part of the fraction

Sometimes there is a fraction under the radical sign (that's what we call the square root symbol)

​

​Square root of a fraction

What happens if there is a fraction??

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Like this:

6/8 = 3/4

​

​Since the square root of 36 is 6 and square root of 64

is 8, you just write those numbners in the for of a fraction

since they were already in a fracrtion.

​

If it need to be reduced, you still have to reduce it.

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Multiple Choice

$$\sqrt[]{\frac{\text{16}}{\text{81}}}$$   

• 4 • 9 = 36

• $$\frac{4}{9}$$  

• 4

• 9

Multiple Choice

$$\sqrt[]{\frac{9}{100}}$$  

• $$\frac{9}{10}$$  

• $$\frac{3}{10}$$  

• $$3$$  

• $$\sqrt[]{9}-10$$  

n³ is n cubed

Cubed?

Like the square which multiplies a number by itself and is therefore called a square, we say that we "cube" a number when it is a number multiplied by itself 3 times because a cube has same lenth sides, and to find its volume you must multiply its height by its length by its width - so the same number times itself 3 times (n • n n or n³)

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