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42 votes
Multiply and Simplify
√45 x √96

User Mhouglum
by
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2 Answers

13 votes
13 votes


{ \qquad\qquad\huge\underline{{\sf Answer}}}

Let's get it done ~


\qquad \sf  \dashrightarrow \: √(45) * √(96)


\qquad \sf  \dashrightarrow \: \sqrt{ {3}^(2) * 5 } * \sqrt{2 {}^(4) * 2 * 3}


\qquad \sf  \dashrightarrow \: 3 √(5) * 2 {}^(2) √(6)


\qquad \sf  \dashrightarrow \: 3 √(5) * 4√(6)


\qquad \sf  \dashrightarrow \: 12 √(30)

User Pleluron
by
1.8k points
13 votes
13 votes

Answer:


12√(30)

Explanation:

Given:


√(45) * √(96)

Rewrite 45 as 9 · 5 and 96 as 16 · 6:


\implies √(9 \cdot 5) * √(16 \cdot 6)


\textsf{Apply radical rule} \quad √(a \cdot b)=√(a)√(b):


\implies √(9)√(5) * √(16)√(6)

Rewrite 9 as 3² and 16 as 4²:


\implies √(3^2)√(5) * √(4^2)√(6)


\textsf{Apply radical rule} \quad √(a^2)=a, \quad a \geq 0


\implies 3√(5) * 4√(6)

Multiply 3 and 4:


\implies 12√(5)√(6)


\textsf{Apply radical rule} \quad √(a)√(b)=√(a \cdot b)


\implies 12√(5 \cdot 6)

Multiply 5 and 6:


\implies 12√(30)

User JLM
by
3.1k points