Evaluating the Squared Term

Oct 13, 2025 by windailys.com 70 views

Understanding the Problem

The given problem involves simplifying an expression that includes a squared term and a square root. We need to evaluate the expression $(-3)^2+\sqrt{48}$ and round off the answer to the nearest whole number.

Evaluating the Squared Term

The first step is to evaluate the squared term $(-3)^2$ . When a negative number is squared, the result is always positive. Therefore, $(-3)^2 = 9$ .

Evaluating the Square Root

The next step is to evaluate the square root of 48. The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, we need to find the square root of 48.

Simplifying the Square Root

To simplify the square root of 48, we can break it down into its prime factors. The prime factorization of 48 is $2^4 \times 3$ . Therefore, the square root of 48 can be written as $\sqrt{2^4 \times 3}$ .

Using the Properties of Square Roots

We can use the properties of square roots to simplify the expression further. The square root of a product is equal to the product of the square roots. Therefore, we can write $\sqrt{2^4 \times 3}$ as $\sqrt{2^4} \times \sqrt{3}$ .

Evaluating the Square Root of 2^4

The square root of $2^4$ is equal to $2^2$ , which is equal to 4.

Evaluating the Square Root of 3

The square root of 3 is an irrational number that cannot be expressed as a finite decimal or fraction.

Simplifying the Expression

Now that we have evaluated the squared term and the square root, we can simplify the expression. We have $(-3)^2+\sqrt{48} = 9 + \sqrt{48}$ . We can substitute the value of $\sqrt{48}$ as $4\sqrt{3}$ .

Evaluating the Expression

Now we can evaluate the expression $9 + 4\sqrt{3}$ . To do this, we need to find the decimal equivalent of $4\sqrt{3}$ .

Finding the Decimal Equivalent of 4\sqrt{3}

To find the decimal equivalent of $4\sqrt{3}$ , we can multiply the square root of 3 by 4. The square root of 3 is approximately equal to 1.732. Therefore, $4\sqrt{3}$ is approximately equal to 6.928.

Evaluating the Expression

Now we can evaluate the expression $9 + 4\sqrt{3}$ . We have $9 + 4\sqrt{3} = 9 + 6.928 = 15.928$ .

Rounding Off the Answer

Finally, we need to round off the answer to the nearest whole number. The nearest whole number to 15.928 is 16.

Conclusion

In conclusion, the simplified expression is $(-3)^2+\sqrt{48} = 16$ .

Frequently Asked Questions

Q: What is the simplified expression for $(-3)^2+\sqrt{48}$ ?

A: The simplified expression is $(-3)^2+\sqrt{48} = 16$ .

Q: How do you evaluate the square root of 48?

A: To evaluate the square root of 48, we can break it down into its prime factors. The prime factorization of 48 is $2^4 \times 3$ . Therefore, the square root of 48 can be written as $\sqrt{2^4 \times 3}$ .

Q: How do you simplify the square root of 48?

A: We can use the properties of square roots to simplify the expression further. The square root of a product is equal to the product of the square roots. Therefore, we can write $\sqrt{2^4 \times 3}$ as $\sqrt{2^4} \times \sqrt{3}$ .

Q: What is the decimal equivalent of $4\sqrt{3}$ ?

A: The decimal equivalent of $4\sqrt{3}$ is approximately equal to 6.928.

Q: How do you round off the answer to the nearest whole number?

A: To round off the answer to the nearest whole number, we need to look at the decimal part of the number. If the decimal part is less than 0.5, we round down to the nearest whole number. If the decimal part is greater than or equal to 0.5, we round up to the nearest whole number.

Final Answer

The final answer is $\boxed{16}$ .

Understanding the Problem

Evaluating the Squared Term

The first step is to evaluate the squared term $(-3)^2$ . When a negative number is squared, the result is always positive. Therefore, $(-3)^2 = 9$ .

Evaluating the Square Root

Simplifying the Square Root

Using the Properties of Square Roots

Evaluating the Square Root of 2^4

The square root of $2^4$ is equal to $2^2$ , which is equal to 4.

Evaluating the Square Root of 3

The square root of 3 is an irrational number that cannot be expressed as a finite decimal or fraction.

Simplifying the Expression

Evaluating the Expression

Now we can evaluate the expression $9 + 4\sqrt{3}$ . To do this, we need to find the decimal equivalent of $4\sqrt{3}$ .

Finding the Decimal Equivalent of 4\sqrt{3}

Evaluating the Expression

Now we can evaluate the expression $9 + 4\sqrt{3}$ . We have $9 + 4\sqrt{3} = 9 + 6.928 = 15.928$ .

Rounding Off the Answer

Finally, we need to round off the answer to the nearest whole number. The nearest whole number to 15.928 is 16.

Conclusion

In conclusion, the simplified expression is $(-3)^2+\sqrt{48} = 16$ .

Frequently Asked Questions

Q: What is the simplified expression for $(-3)^2+\sqrt{48}$ ?

A: The simplified expression is $(-3)^2+\sqrt{48} = 16$ .

Q: How do you evaluate the square root of 48?

Q: How do you simplify the square root of 48?

Q: What is the decimal equivalent of $4\sqrt{3}$ ?

A: The decimal equivalent of $4\sqrt{3}$ is approximately equal to 6.928.

Q: How do you round off the answer to the nearest whole number?

Q&A Section

Q: What is the difference between a squared term and a square root?

A: A squared term is a number that has been multiplied by itself, while a square root is a value that, when multiplied by itself, gives the original number.

Q: How do you simplify a square root?

A: We can use the properties of square roots to simplify the expression further. The square root of a product is equal to the product of the square roots.

Q: What is the prime factorization of 48?

A: The prime factorization of 48 is $2^4 \times 3$ .

Q: How do you evaluate the square root of 3?

A: The square root of 3 is an irrational number that cannot be expressed as a finite decimal or fraction.

Q: What is the decimal equivalent of $4\sqrt{3}$ ?

A: The decimal equivalent of $4\sqrt{3}$ is approximately equal to 6.928.

Q: How do you round off the answer to the nearest whole number?

Final Answer

The final answer is $\boxed{16}$ .