# Square roots and cube roots explained. Work out root 36 or cube root of 27.

First of all let’s take a look at square roots.

If you want to find a square root of a number then you need to look for a number when multiplied by itself to give the number that you are square rooting.

So if you have √a then ? × ? = a

Let’s cover a few questions:

**Question 1**

Work out √16 (this means the square root of 16)

Since 4 × 4 = 16 then the square root of 16 is 4.

**Question 2**

Work out √49

Since 7 × 7 = 49 then the square root of 49 is 7.

**Question 3**

Work out √225

Since 15 × 15 = 225 then the square root of 225 is 15.

**Question 4**

Work out √1

Since 1 × 1 = 1 then the square root of 1 is 1.

**Question 5**

Work out √144

Since 12 × 12 = 144 then the square root of 144 is 12.

Let’s now look at cube roots. This time you are looking for a number such that ? × ? × ? gives the number that you are cube rooting. Let’s go over a few questions of cube roots:

**Question 6**

Work out ³√27 (that is the cube root of 27)

So you are looking for a number such that ? × ? × ? = 27. The number that you looking for is 3 because 3 × 3 × 3 = 27 (3 × 3 = 9 so 9 × 3 = 27). Therefore the cube root of 27 is 3.

**Question 7**

Work out ³√8 (that is the cube root of 8)

So you are looking for a number such that ? × ? × ? = 8. The number that you looking for is 8 because 2 × 2 × 2 = 8 (2 × 2 = 4 so 4 × 2 = 8). Therefore the cube root of 8 is 2.

**Question 8**

Work out ³√64 (that is the cube root of 64)

So you are looking for a number such that ? × ? × ? = 64. The number that you looking for is 4 because 4 × 4 × 4 = 64 (4 × 4 = 16 so 16 × 4 = 64). Therefore the cube root of 64 is 4.

**Question 9**

Work out ³√125 (that is the cube root of 125)

So you are looking for a number such that ? × ? × ? = 125. The number that you looking for is 5 because 5 × 5 × 5 = 125 (5 × 5 = 25 so 25 × 5 = 125). Therefore the cube root of 125 is 5.

**Question 10**

Work out ³√-8 (that is the cube root of negative 8)

So you are looking for a number such that ? × ? × ? = -8. The number that you looking for is -2 because -2 × -2 × -2 = -8 (-2 × -2 = 4 so 4 × -2 = -8). Therefore the cube root of -8 is -2.

**So to summarise if you are taking the square root of a number then you are looking for a number such that ? × ? = the number you are rooting. And if you are taking the cube root of a number then you are looking for a number such that ? × ? × ? = the number that you are cube rooting. **