The question
Question: simplify √50 over √2.
√50√2
1 One root
Rule: a root over a root is the root of the fraction.
√a√b = √ab
So we write one root over the fraction.
= √502
50 divided by 2 is 25.
50 ÷ 2 = 25
So we get √25.
= √25
2 Simplify the root
25 is a square number: 5 times 5 is 25.
So √25 is 5.
5 × 5 = 25
So we get 5.
So the answer is 5.
= 5
Careful!
50 divided by 2 is 25.
But the answer is the ROOT of 25.
Don't drop the root.
Careful: not √50√2 = 25 ✗
3 Check
Let's check with a calculator.
The start is about 5.00.
Start: √50√2 ≈ 5.00
The answer is about 5.00 too.
So it is right!
Answer: 5 ≈ 5.00
Let's look back.
First: one root.
Then: simplify the root.
Last: check.
▶ Watch it solved
The question
Question: simplify √60 over √5.
√60√5
1 One root
Rule: a root over a root is the root of the fraction.
√a√b = √ab
So we write one root over the fraction.
= √605
60 divided by 5 is 12.
60 ÷ 5 = 12
So we get √12.
= √12
2 Simplify the root
Now we make √12 simpler, like in the lesson on square roots.
The biggest square that goes into 12 is 4: 12 divided by 4 is 3.
Square numbers: 4
12 ÷ 4 = 3 ✓
So √12 is √4 times √3.
= √4 × √3
√4 is 2, because 2 times 2 is 4.
2 × 2 = 4
So we get 2√3.
So the answer is 2√3.
= 2√3
Careful!
60 divided by 5 is 12.
But the answer is the ROOT of 12.
Don't drop the root.
Careful: not √60√5 = 12 ✗
3 Check
Let's check with a calculator.
The start is about 3.46.
Start: √60√5 ≈ 3.46
The answer is about 3.46 too.
So it is right!
Answer: 2√3 ≈ 3.46
Let's look back.
First: one root.
Then: simplify the root.
Last: check.
▶ Watch it solved
The question
Question: simplify 4 over √8.
4√8
1 Simplify the bottom first
Simplify the bottom root first.
It keeps the numbers small.
8 is 4 times 2, and √4 is 2.
So √8 is 2√2.
√8 = √4 × √2 = 2√2
So the bottom is 2√2.
= 42√2
2 Remove the root at the bottom
A root times itself is the number inside: √2 times √2 is 2.
So we multiply the bottom by √2.
√2 × √2 = 2
To keep the fraction the same, we multiply the top by √2 too.
√2 over √2 is 1, and times 1 changes nothing.
√2√2 = 1
So we multiply by √2 over √2.
= 42√2 × √2√2
Careful!
Many people multiply only the bottom.
Then the fraction changes.
Top and bottom get the same √2.
Careful: multiply the TOP by the root too
On top: 4 times √2 is 4√2.
On the bottom: 2 times 2 is 4.
No root at the bottom now.
= 4√24
3 Cancel
4 and 4 can both be divided by 4.
4/4 is 1.
4 ÷ 4 = 1, 4 ÷ 4 = 1
So we get √2.
= √2
4 Check
Let's check with a calculator.
The start is about 1.41.
Start: 4√8 ≈ 1.41
The answer is about 1.41 too.
So it is right!
Answer: √2 ≈ 1.41
Let's look back.
First: simplify the bottom first.
Then: remove the root at the bottom.
Then: cancel.
Last: check.
▶ Watch it solved
