All expressions were simplified using the basics of surds.
What are surds?
A surd is an expression that includes a square root, cube root, etc.
1) √5+6√5
Take √5 as a common term.
=√5(1+6)
=7√5
2) 4√2-7√2
Take √2 as a common term
=√2(4-7)
=-3√2
3)3√7-√63
We know that√63 =3√7
=3√7-3√7
=0
4)-6√10+5√90
We know that√90 = 3√10
=-6√10+5*3√10
9√10
5)√6(√2+√3)
=√12 + √18
2√3+3√3
6)3√7(1-√7)
=3√7-3√7*√7
=3√7-21
7) (√6+√3)(√2-2)
=√6*√2-√6*2+√3*√2-√3*2
=√12-2√6+√6-2√3
=2√3-2√6+√6-2√3
=-√6
8)3/(√7-√3)
Multiply both numerator and denominator by (√7+√3).
=[3(√7+√3)]/[(√7-√3)(√7+√3)]
=[3√7+3√3]/4
9)r₁/r₂=√m₂/m₁
It is given that m₁=12 & m₂=30
So, r₁/r₂=√30/12
r₁/r₂=√5/2
r₁/r₂=(√5*√2)/(√2*√2)
r₁/r₂=√10/2
10)(√3+√5)^2
=(√3)^2 + (√5)^2+2*√3*√5
=8+2√15
Thus, All expressions were simplified using the basics of surds.
To get more about surds visit:
https://brainly.com/question/24700530
