How do you simplify #5sqrt(3x^3)+2sqrt(27x)#?

Answer 1

See a solution process below:

Step 1: Rewrite the radicals to make them simpler, then apply this rule to radicals:

#sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))#
#5sqrt(color(red)(x^2) * color(blue)(3x)) + 2sqrt(color(red)(9) * color(blue)(3x)) =>#
#5sqrt(color(red)(x^2))sqrt(color(blue)(3x)) + 2sqrt(color(red)(9))sqrt(color(blue)(3x)) =>#
#5xsqrt(color(blue)(3x)) + (2 * 3)sqrt(color(blue)(3x)) =>#
#5xsqrt(color(blue)(3x)) + 6sqrt(color(blue)(3x))#
Step 2) Combine like terms by factoring out the common term: #sqrt(color(blue)(3x))# :
#(5x + 6)sqrt(color(blue)(3x))#
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Answer 2

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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Answer from HIX Tutor

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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