What is \(4 \sqrt{45} - 7 \sqrt{5}\) ?
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Detailed Explanation
To subtract these radicals together their radicals must be the same:
\([4 \sqrt{45} - 7 \sqrt{5}] \)
= \(4 \sqrt{ 3^2 \times 5 } - 7 \sqrt{5} \)
= 4 (\(\sqrt{3^2}\) × \(\sqrt{5}\)) - \(7 \sqrt{5} \)
= \(4 \times 3 \sqrt{5} - 7 \sqrt{5} \)
= \(5 \sqrt{5} \)
\([4 \sqrt{45} - 7 \sqrt{5}] \)
= \(4 \sqrt{ 3^2 \times 5 } - 7 \sqrt{5} \)
= 4 (\(\sqrt{3^2}\) × \(\sqrt{5}\)) - \(7 \sqrt{5} \)
= \(4 \times 3 \sqrt{5} - 7 \sqrt{5} \)
= \(5 \sqrt{5} \)
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