Answer:
The value of a is 7
Step-by-step explanation:
[tex] \sqrt{2} ( \sqrt{45} + \sqrt{80} )[/tex]
Transform the expression
[tex] \sqrt{2} \times ( \sqrt{ {3}^{2} \times 5} + \sqrt{ {4}^{2} \times 5 } [/tex]
Rewrite the expression
[tex] \sqrt{2} \times ( \sqrt{ {3}^{2} } \times \sqrt{5} + \sqrt{ {4}^{2} } \times \sqrt{5} [/tex]
Simplify the radical expression
[tex] \sqrt{2} \times (3 \sqrt{5} + 4 \sqrt{5} [/tex]
Expand the Expression
[tex]3 \sqrt{10} + 4 \sqrt{10} [/tex]
Combine like terms
[tex]7 \sqrt{10} [/tex]
Comparing with [tex] a \sqrt{10} [/tex]
a = 7
