MATH SOLVE

5 months ago

Q:
# 1. Simplify 2/radical 52. Simplify -11 radical 1123. Simplify 17 radical 17 -9 radical 174. Simplify 6/ radical 3+2

Accepted Solution

A:

1. (2√5)/5

2. -44√7

3. 8√17

4. -6√3+12

For 1: Multiply the numerator and denominator by √5:

[tex]\frac{2}{\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{5}}=\frac{2\sqrt{5}}{5}[/tex]

For 2: Simplify √112:

√112 = √(2*56) = √(2*2*28) = √(4*4*7) = 2*2√7 = 4√7

Now multiply by the -11 coefficient:

-11(4√7) = -44√7

For 3: Add the radicals as you would variables that are like terms.

For 4: Multiply by the conjugate. The conjugate of the denominator has the same values with the sign of the radical changed:

[tex]\frac{6}{\sqrt{3}+2}\times \frac{\sqrt{3}-2}{\sqrt{3}-2}=\frac{6(\sqrt{3}-2)}{(\sqrt{3}+2)(\sqrt{3}-2)} \\ \\=\frac{6\sqrt{3}-6*2}{\sqrt{3}*\sqrt{3}-2\sqrt{3}+2\sqrt{3}-2*2} \\ \\=\frac{6\sqrt{3}-12}{3-4}=\frac{6\sqrt{3}-12}{-1}=-6\sqrt{3}+12[/tex]

2. -44√7

3. 8√17

4. -6√3+12

For 1: Multiply the numerator and denominator by √5:

[tex]\frac{2}{\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{5}}=\frac{2\sqrt{5}}{5}[/tex]

For 2: Simplify √112:

√112 = √(2*56) = √(2*2*28) = √(4*4*7) = 2*2√7 = 4√7

Now multiply by the -11 coefficient:

-11(4√7) = -44√7

For 3: Add the radicals as you would variables that are like terms.

For 4: Multiply by the conjugate. The conjugate of the denominator has the same values with the sign of the radical changed:

[tex]\frac{6}{\sqrt{3}+2}\times \frac{\sqrt{3}-2}{\sqrt{3}-2}=\frac{6(\sqrt{3}-2)}{(\sqrt{3}+2)(\sqrt{3}-2)} \\ \\=\frac{6\sqrt{3}-6*2}{\sqrt{3}*\sqrt{3}-2\sqrt{3}+2\sqrt{3}-2*2} \\ \\=\frac{6\sqrt{3}-12}{3-4}=\frac{6\sqrt{3}-12}{-1}=-6\sqrt{3}+12[/tex]