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oee [108]
3 years ago
12

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

Mathematics
2 answers:
e-lub [12.9K]3 years ago
8 0

Answer:

7

Step-by-step explanation:

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

7√10= a√10

a=7

aleksandrvk [35]3 years ago
4 0

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

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