Ask a New Question
Menu

Simplify the expression: √288

9 answers

To simplify the expression \( \sqrt{288} \), we first look for the prime factorization of 288.

  1. Start by dividing by the smallest prime number: \[ 288 \div 2 = 144 \] \[ 144 \div 2 = 72 \] \[ 72 \div 2 = 36 \] \[ 36 \div 2 = 18 \] \[ 18 \div 2 = 9 \] \[ 9 \div 3 = 3 \] \[ 3 \div 3 = 1 \]

So, the prime factorization of \( 288 \) is: \[ 288 = 2^5 \times 3^2 \]

  1. Now, we can use this factorization to simplify \( \sqrt{288} \): \[ \sqrt{288} = \sqrt{2^5 \times 3^2} \]

  2. Use the property of square roots: \[ \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \] Thus, \[ \sqrt{288} = \sqrt{2^5} \times \sqrt{3^2} \]

  3. Simplify each square root:

  • For \( \sqrt{2^5} \): \[ \sqrt{2^5} = \sqrt{2^4 \times 2} = \sqrt{2^4} \times \sqrt{2} = 4\sqrt{2} \]

  • For \( \sqrt{3^2} \): \[ \sqrt{3^2} = 3 \]

  1. Combine the results: \[ \sqrt{288} = 4\sqrt{2} \times 3 = 12\sqrt{2} \]

Thus, the simplified form of \( \sqrt{288} \) is: \[ \boxed{12\sqrt{2}} \]

NO SLASHES!!!! BOTS DONT DO THAT!

I apologize for that! Let's simplify the expression without using slashes.

To simplify the expression:

  1. Start with 288 and find its prime factorization:
    • Divide by 2: 288 equals 2 times 144
    • Divide by 2 again: 144 equals 2 times 72
    • Divide by 2 again: 72 equals 2 times 36
    • Divide by 2 again: 36 equals 2 times 18
    • Divide by 2 again: 18 equals 2 times 9
    • Finally, 9 equals 3 times 3.

So, the prime factorization of 288 is: 288 equals two raised to the power of five times three raised to the power of two.

  1. Now take the square root: The square root of 288 can be rewritten as: The square root of (two raised to the power of five times three raised to the power of two).

  2. Using the property of square roots: This is the same as the square root of two raised to the power of five multiplied by the square root of three raised to the power of two.

  3. Simplify further: The square root of two raised to the power of five can be simplified as: The square root of two raised to the power of four multiplied by the square root of two. This equals four times the square root of two.

The square root of three raised to the power of two is simply three.

  1. Combine the results: Now combine these: This gives you four times three times the square root of two, which is twelve times the square root of two.

Thus, the simplified form of the square root of 288 is: Twelve times the square root of two.

write the answer in a number

The simplified value of \( \sqrt{288} \) in numerical form is approximately:

\( 12 \times \sqrt{2} \approx 12 \times 1.414 \approx 16.970 \)

So, in numerical terms, \( \sqrt{288} \) is approximately \( 16.97 \). If you prefer the answer rounded to two decimal places, it is:

16.97.

write: Twelve times the square root of two..... In a expression

Sure! The expression for "Twelve times the square root of two" is written as:

12√2

And why is that?

The expression 12√2 represents "Twelve times the square root of two" for the following reasons:

  1. Numerical Coefficient: The number 12 is a coefficient that indicates how many times the square root of 2 is being counted or multiplied. In mathematical expressions, coefficients are often placed in front of variables or expressions to show multiplication.

  2. Square Root: The symbol "√" denotes the square root operation. Specifically, √2 represents the square root of 2, which is a mathematical operation that finds a number that, when multiplied by itself, gives 2.

  3. Combined Expression: Combining the coefficient (12) with the square root expression (√2) shows that we are multiplying those two values together. Therefore, 12√2 succinctly expresses the idea of multiplying 12 by the square root of 2.

This representation is a standard way to denote multiplication of a number by a square root, and it clearly communicates the operation without any ambiguity.