How do you simplify #5sqrt(3x^3)+2sqrt(27x)#?
See a solution process below:
Step 1: Rewrite the radicals to make them simpler, then apply this rule to radicals:
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To simplify the expression 5√(3x^3) + 2√(27x), we can start by simplifying the square roots separately.
First, let's simplify 5√(3x^3):
- The square root of 3x^3 can be broken down as the square root of 3 times the square root of x^3.
- The square root of x^3 can be further simplified as x times the square root of x.
- Therefore, 5√(3x^3) becomes 5√3 * x√x.
Next, let's simplify 2√(27x):
- The square root of 27x can be broken down as the square root of 27 times the square root of x.
- The square root of 27 can be simplified as 3 times the square root of 3.
- Therefore, 2√(27x) becomes 2 * 3√3 * √x.
Now, we can combine the simplified expressions: 5√(3x^3) + 2√(27x) simplifies to 5√3 * x√x + 2 * 3√3 * √x.
Since both terms have a common factor of √x, we can factor it out: 5√3 * x√x + 2 * 3√3 * √x = (√x)(5√3 * x + 2 * 3√3).
Therefore, the simplified expression is (√x)(5√3 * x + 2 * 3√3).
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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.
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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