Rewrite each of the following radicals as a rational number or in simplest radical form. a. √3(√3-1)b. (5+√3)²c. (10+√11)(10-√11)

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

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step-by-step explanation:

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