Question
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Answer
\( 10\sqrt{3} \)
Solution
Calculate or simplify the expression \( \sqrt{6} \times \sqrt{5} \times \sqrt{10} \).
Calculate the value by following steps:
- step0: Calculate:
\(\sqrt{6}\times \sqrt{5}\times \sqrt{10}\)
- step1: Multiply the terms:
\(\sqrt{30}\times \sqrt{10}\)
- step2: Use the properties of radicals:
\(\sqrt{30\times 10}\)
- step3: Calculate:
\(\sqrt{300}\)
- step4: Write as a product:
\(\sqrt{100\times 3}\)
- step5: Write in exponential form:
\(\sqrt{10^{2}\times 3}\)
- step6: Use the properties of radicals:
\(\sqrt{10^{2}}\times \sqrt{3}\)
- step7: Simplify the root:
\(10\sqrt{3}\)
The result of \( \sqrt{6} \times \sqrt{5} \times \sqrt{10} \) is \( 10\sqrt{3} \).
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Simplify this solution Mind Expander
Did you know that when multiplying square roots, you can combine them under one radical? So, \( \sqrt{6} \times \sqrt{5} \times \sqrt{10} \) becomes \( \sqrt{6 \times 5 \times 10} \). That’s like finding the treasure of all those numbers together! Now, let's calculate that treasure: \( 6 \times 5 = 30 \) and \( 30 \times 10 = 300 \). So you have \( \sqrt{300} \). A little more fun fact—300 can also be simplified, as it equals \( 100 \times 3 \), giving you \( 10\sqrt{3} \). That’s the beauty of square roots!
