Question

Add 5√10 + √10. Choose the correct answer from below:

√25
6√20
6√10
√60

Answer 1

[AI-generated answer — Bot GPT 3.5]

5√10 + √10 = 6√10

Answer 2

Subtract 11√9 - 5√9.

What is the difference?

Answer 3

[AI-generated answer — Bot GPT 3.5]

11√9 - 5√9 = 6√9.

However, it is important to simplify the square root of 9. The square root of 9 is 3.
So, 6√9 = 6(√3) = 6√3.

Answer 4

Multiply (5√19) x (6√2). Give an exact answer.

Answer 5

[AI-generated answer — Bot GPT 3.5]

(5√19) x (6√2) = 30√38

Answer 6

Divide √95/3√5 (95 square rooted over 3 and 5 square rooted in fraction). Provide an exact answer.

Answer 7

[AI-generated answer — Bot GPT 3.5]

To divide √95 by 3√5, we can multiply both the numerator and the denominator of the fraction by the conjugate of the denominator, which is 3√5.

√95/3√5 = (√95 * 3√5)/(3√5 * 3√5)

Simplifying the numerator:
√95 * 3√5 = 3√(95 * 5)
= 3√(475)
= 3√(25 * 19)
= 3(√25 * √19)
= 3(5√19)
= 15√19

Simplifying the denominator:
3√5 * 3√5 = 3√(5 * 5)
= 3√25
= 3*5
= 15

So the entire expression becomes:
√95/3√5 = 15√19/15

The 15 in the numerator and denominator cancels out:
√95/3√5 = √19/1
= √19

Answer 8

Divide 36√39/9√13 (36 and 39 square rooted over 9 and 13 square rooted in fraction). Provide an exact answer.

Answer 9

[AI-generated answer — Bot GPT 3.5]

To divide 36√39 by 9√13, we can simplify the expression by canceling out common factors in the numerator and denominator.

36√39 / 9√13 = (36/9) * (√39 / √13)

Simplifying the numerator:
36/9 = 4

Simplifying the denominator:
√39 / √13 = √(39/13) = √3

So the entire expression becomes:
4√3 / 1 = 4√3

Therefore, the exact answer is 4√3.

Answer 10

Simplify √48.

Answer 11

[AI-generated answer — Bot GPT 3.5]

To simplify √48, we can look for perfect square factors of 48.

Breaking down 48 into its prime factors: 48 = 2 * 2 * 2 * 2 * 3

Taking out pairs of 2 to simplify the square root:
√48 = √(2 * 2 * 2 * 2 * 3) = √(2 * 2 * 2 * 2) * √3 = 4√3

So, the simplified form of √48 is 4√3.

Answer 12

Simplify ∛54.

Answer 13

[AI-generated answer — Bot GPT 3.5]

To simplify ∛54, we need to find the prime factors of 54.

The prime factorization of 54 is 2 * 3 * 3 * 3.

Next, we group the factors into threes:
∛54 = ∛(2 * 3 * 3 * 3) = ∛(2 * 3^3)

Taking out one factor of 3:
∛54 = ∛2 * ∛(3^3) = ∛2 * 3 = 3∛2

Therefore, the simplified form of ∛54 is 3∛2.

Answer 14

Find the square root of 169: √169. Choose the correct answer from below.

-13
84.5
13, -13
13

Answer 15

[AI-generated answer — Bot GPT 3.5]

The correct answer is 13.

Answer 16

Find the cube root of -729: ∛-729. Choose the correct answer from below:

9, -9
-9
243
9

Answer 17

[AI-generated answer — Bot GPT 3.5]

The correct answer is -9.

Answer 18

Find the cube root of -8: ∛-8.

Answer 19

[AI-generated answer — Bot GPT 3.5]

The cube root of -8 is -2.

Answer 20

What is the irrational square root √63 rewritten as the product of an integer and another irrational square root, in simplest form?

Answer 21

[AI-generated answer — Bot GPT 3.5]

√63 can be rewritten as √(9 * 7) since 9 is a perfect square. This can be further simplified as √9 * √7, which equals 3√7.

Therefore, the irrational square root √63 can be rewritten as the product of an integer, 3, and another irrational square root, √7.

Answer 22

What is the irrational cube root ∛81 rewritten as the product of an integer and another irrational cube root?

Answer 23

[AI-generated answer — Bot GPT 3.5]

∛81 can be rewritten as the product of an integer and another irrational cube root by factoring 81 into its prime factors.

The prime factorization of 81 is 3 * 3 * 3 * 3.

Taking out one factor of 3, we have ∛81 = ∛(3 * 3 * 3 * 3) = ∛(3^4).

Simplifying further, we can rewrite ∛81 as 3∛3.

Therefore, the irrational cube root ∛81 is rewritten as the product of an integer, 3, and another irrational cube root, ∛3.

Answer 24

Find the cubic root of 135: ∛135. Choose the correct answer from below:

3∛5
3√5
5∛27
∛5

Answer 25

[AI-generated answer — Bot GPT 3.5]

The cubic root of 135 is 5∛3.

Answer 26

Choose one from the question though

Answer 27

[AI-generated answer — Bot GPT 3.5]

Apologies for the oversight. The correct answer is 3∛5.

Answer 28

What is the circumference of a circle with a diameter of 4.5 miles? Estimate the circumference to the hundredths place using 3.14 for π. Choose an answer from below:

63.59 miles
14.2 miles
7.07 miles
1413 miles

Answer 29

[AI-generated answer — Bot GPT 3.5]

The circumference of a circle can be calculated using the formula C = πd, where C is the circumference and d is the diameter.

Given that the diameter is 4.5 miles, we can calculate the circumference as:

C = 3.14 * 4.5 = 14.13

Rounded to the hundredths place, the estimated circumference is 14.13 miles.

Therefore, the closest answer from the options provided is 14.2 miles.

Answer 30

What is the irrational cube root ∛189 rewritten as the product of an integer and another irrational cube root? Please show your work.

Answer 31

[AI-generated answer — Bot GPT 3.5]

To rewrite ∛189 as the product of an integer and another irrational cube root, we need to factor 189 into its prime factors.

The prime factorization of 189 is 3 * 3 * 3 * 7.

Taking out one factor of 3, we have ∛189 = ∛(3 * 3 * 3 * 7) = ∛(3^3 * 7).

Next, we can rewrite ∛189 as 3∛7.

Therefore, the irrational cube root ∛189 is rewritten as the product of an integer, 3, and another irrational cube root, ∛7.