# How do you multiply #sqrt[27b] * sqrt[3b^2L]#?

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To multiply (\sqrt{27b}) by (\sqrt{3b^2L}), you can first simplify each square root individually:

- (\sqrt{27b} = \sqrt{9 \times 3 \times b} = \sqrt{9} \times \sqrt{3} \times \sqrt{b} = 3\sqrt{3b})
- (\sqrt{3b^2L} = \sqrt{3 \times b \times b \times L} = \sqrt{3} \times \sqrt{b} \times \sqrt{b} \times \sqrt{L} = b\sqrt{3L})

Then, multiply the simplified expressions together:

[3\sqrt{3b} \times b\sqrt{3L} = 3b \times \sqrt{3b} \times \sqrt{3L} = 3b \times \sqrt{(3b)(3L)} = 3b\sqrt{9bL} = 3b \times 3\sqrt{bL} = 9b\sqrt{bL}]

So, the product of (\sqrt{27b}) and (\sqrt{3b^2L}) is (9b\sqrt{bL}).

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