Question

√2 (√45 + √80) can be written in the form a√10 where a is an integer. Find the value of a.

Answer 1

Answer:

a = 7

Step-by-step explanation:

Using the rule of radicals

$\sqrt{a}$ × $\sqrt{b}$ ⇔ $\sqrt{ab}$

Given

$\sqrt{2}$ ($\sqrt{45}$ + $\sqrt{80}$ ) ← distribute parenthesis by $\sqrt{2}$

= $\sqrt{90}$ + $\sqrt{160}$

= $\sqrt{9(10)}$ + $\sqrt{16(10)}$

= $\sqrt{9}$ × $\sqrt{10}$ + ($\sqrt{16}$ × $\sqrt{10}$ )

= 3$\sqrt{10}$ + 4$\sqrt{10}$

= 7$\sqrt{10}$ → in the form a$\sqrt{10}$

with a = 7

Answer 2

Answer:

7

Step-by-step explanation:

√2 (√45 + √80) = √90+√160= 3√10+4√10= 7√10

7√10= a√10

a=7