Question

PLEASEEEEE

Match the expressions with their simplified versions.

Answer 1

1.
`\\ormalsize \boxed{\textsf{$4√(2)\cdot√(2)$}} \implies \boxed{8}`

2.
`\\ormalsize \boxed{\textsf{$3√(7)-2√(7)$}} \implies \\ormalsize \boxed{\textsf{$√(7)$}}`

3.
`\\ormalsize \boxed{\textsf{$(√(7))/(2√(7))$}} \implies \\ormalsize \boxed{\textsf{$(1)/(2)$}}`

4.
`\\ormalsize \boxed{\textsf{$2√(5)\cdot 2√(5)$}} \implies \boxed{20}`

Explanation:

The Radical Rules by Lial et al. (2017) state that:

Product rule:
`\large \textsf{$\sqrt[n]{a}\cdot\sqrt[n]{b}=\sqrt[n]{ab}$}`

• "The product of two roots is the root of the product."

Quotient rule:
`\large \textsf{$\sqrt[n]{(a)/(b)}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}$}\ \ \textsf{$(b \\eq 0)$}`

• "The root of a quotient is the quotient of the roots."

1.

`\implies \\ormalsize \textsf{$4√(2)\cdot√(2)$}\\\\\\ormalsize \implies \textsf{$4√(2\cdot2)$}\\\\ \implies \\ormalsize \textsf{$4√(4)$}\\\\ \implies\\ormalsize \textsf{$4\cdot 2 = 8$}`

`\\ormalsize \boxed{\textsf{$4√(2)\cdot√(2)$}} \implies \boxed{8}`

2.

`\implies \\ormalsize \textsf{$3√(7)-2√(7)$}\\\\ \implies\\ormalsize \textsf{$(3-2)√(7)$}\\\\ \implies\\ormalsize \textsf{$1√(7)$}\\\\ \implies\\ormalsize \textsf{$√(7)$}`

`\\ormalsize \boxed{\textsf{$3√(7)-2√(7)$}} \implies \\ormalsize \boxed{\textsf{$√(7)$}}`

3.

`\implies \\ormalsize \textsf{$(√(7))/(2√(7))$}\\\\\\ \implies\\ormalsize \textsf{$(1√(7))/(2√(7))$}\\\\\\ \implies\\ormalsize \textsf{$(1)/(2)$}\\\\`

`\\ormalsize \boxed{\textsf{$(√(7))/(2√(7))$}} \implies \\ormalsize \boxed{\textsf{$(1)/(2)$}}`

4.

`\implies \\ormalsize \textsf{$2√(5)\cdot 2√(5)$}\\\\ \implies\\ormalsize \textsf{$2\cdot2√(5\cdot5)$}\\\\ \implies \\ormalsize \textsf{$4√(25)$}\\\\ \implies \\ormalsize \textsf{$4\cdot5=20$}\\\\`

`\\ormalsize \boxed{\textsf{$2√(5)\cdot 2√(5)$}} \implies \boxed{20}`

Reference:

Lial, M., Hornsby, J., Schneider, D., & Daniels, C. (2017). College Algebra and Trigonometry, Global Edition (6th ed., p. 94).