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Chapter 0: Problem 40

Add or subtract terms whenever possible. $$\sqrt{63 x}-\sqrt{28 x}$$

Short Answer

Expert verified
\(\sqrt{7x}\)

Step by step solution

01

Factorize the Numbers

Begin by factorizing the numbers inside the square roots in the given expression. In this case, 63 can be factorized into 9*7 and 28 can be factorized into 4*7. So, now the expression can be rewritten as: \(\sqrt{9*7x} - \sqrt{4*7x}\).
02

Apply Square Root Property

The square root property states that \(\sqrt{ab} = \sqrt{a}\sqrt{b}\) if a and b are positive numbers. Utilize this property to further simplify the expression. The expression hence becomes: \(3\sqrt{7x} - 2\sqrt{7x}\).
03

Simplify the Final Result

Now, the expression under the square roots in both terms is the same (7x), which allows us to subtract the numeric coefficients: \(3\sqrt{7x} - 2\sqrt{7x} = (3 - 2)\sqrt{7x} = \sqrt{7x}\)

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Most popular questions from this chapter

Exercises \(142-144\) will help you prepare for the material covered in the next section. Use the distributive property to multiply: $$2 x^{4}\left(8 x^{4}+3 x\right)$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) toproduce a true statement. $$5^{2} \cdot 5^{-2}>2^{5} \cdot 2^{-5}$$

How do you know if a number is written in scientific notation?

Will help you prepare for the material covered in the next section.Exercises \(144-146\) will help you prepare for the material covered in the next section. Factor the numerator and the denominator. Then simplify by dividing out the common factor in the numerator and the denominator. $$ \frac{x^{2}+6 x+5}{x^{2}-25} $$

Simplify using properties of exponents. $$\frac{72 x^{\frac{3}{4}}}{9 x^{\frac{1}{3}}}$$
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