# How do you simplify # sqrt ((4a^3 )/( 27b^3))#?

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Just another way of writing the same thing as the other solution:

You look for numbers that are squared. Take them outside the square root and 'get rid' of the square.

Take the 2 out side the square root giving

Take the squared values outside the square roots giving

So we can multiply by 1 and not change the inherent value but we can change the way it looks.

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To simplify (\sqrt{\frac{4a^3}{27b^3}}), you can follow these steps:

- Rewrite the expression under the square root sign as a fraction: (\frac{4a^3}{27b^3}).
- Factor the numerator and denominator to simplify: (4a^3 = 2^2 \cdot a^3) and (27b^3 = 3^3 \cdot b^3).
- Take the square root of the factors: (\sqrt{2^2 \cdot a^3} = 2a \sqrt{a}) and (\sqrt{3^3 \cdot b^3} = 3b \sqrt{b}).
- Combine the square roots: (\sqrt{\frac{4a^3}{27b^3}} = \frac{2a\sqrt{a}}{3b\sqrt{b}}).
- Simplify the expression by dividing the numerator and denominator by the greatest common factor (GCF), which is 2: (\frac{2a\sqrt{a}}{3b\sqrt{b}} = \frac{a\sqrt{a}}{\frac{3}{2}b\sqrt{b}}).

Therefore, the simplified expression is (\frac{a\sqrt{a}}{\frac{3}{2}b\sqrt{b}}).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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