Simplify 3 square root of 5 end root minus 2 square root of 7 end root plus square root of 45 end root minus square root of 28. 2 square root of 12 2 square root of 2 6 square r…

Question

asked Feb 15, 2019 17.8k views

2 Answers

Anton Babenko · Answer 1 · 2019-02-18T17:05:31+0000

Simplify √ 45 to 3√ 5 and √ 28 to 2√ 7

Which gives you (3√5 +3√ 5 )+(−2√ 7 −2√ 7 )

Combine like terms = 6√ 5 −4√ 7

So the answer would be

6 square root of 5 end root minus 4 square root of 7

Durell · Answer 2 · 2019-02-20T16:31:40+0000

Hence, the simplified expression is:

6 square root of 5 end root minus 4 square root of 7.

i.e.
6√(5)-4√(7)

We are asked to simplify the expression:

3 square root of 5 end root minus 2 square root of 7 end root plus square root of 45 end root minus square root of 28.

which mathematically is given by:

3√(5)-2√(7)+√(45)-√(28)

Since, we know that:

$\sqrt[45}=√(3* 3* 5)\\\\i.e.\\\\√(45)=3√(5)$

and

$√(28)=√(2* 2* 7)\\\\i.e.\\\\√(28)=2√(7)$

i.e. we need to simplify:

3√(5)-2√(7)+3√(5)-2√(7)

Now, we combine the like terms as follows:

$=3√(5)+3√(5)-2√(7)-2√(7)\\\\=6√(5)-4√(7)$