Answer:
a. Rational number 1.26
Simplest radical 3 − √ 3
b. Simplest radical 28 + 10 √ 3
Rational number 45.32
c. Rational number 89
Step-by-step explanation:
a. √3(√3-1)
To get the simplest radical
Apply the distributive property.
√3*√3-√3
Combine using the product rule for radicals.
√ 3*3+√3*−1
Move − 1 to the left of √3.
√ 3*√ 3*3 - 1 *√3
Multiply 3 by 3.
√ 9 − 1 *√ 3
Rewrite 9 as 3 ^2
√3^2 -1 *√ 3
Pull terms out from under the radical, assuming positive real numbers.
3 − 1 *√ 3
Rewrite − 1 √ 3 as − √ 3 .
3 − √ 3
Rational number 1.26
b. (5+√3)²
Expand
(5+√3)²= 25 +5*√3+5*√3+3= 28 + 10 √ 3
Simplest radical 28 + 10 √ 3
Rational number 45.32
c. (10+√11)(10-√11)
Expand
(10+√11)(10-√11)= 10*10+ 10*-√11+10*√11+√11*-√11
=100+ 10*-√11+10*√11- 11
=89- 10*√11+10*√11
=89
