Add 5√10 + √10. Choose the correct answer from below:
√25
6√20
6√10
√60
31 answers
5√10 + √10 = 6√10
Subtract 11√9 - 5√9.
What is the difference?
What is the difference?
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.
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.
Multiply (5√19) x (6√2). Give an exact answer.
(5√19) x (6√2) = 30√38
Divide √95/3√5 (95 square rooted over 3 and 5 square rooted in fraction). Provide an exact answer.
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
√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
Divide 36√39/9√13 (36 and 39 square rooted over 9 and 13 square rooted in fraction). Provide an exact answer.
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.
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.
Simplify √48.
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.
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.
Simplify ∛54.
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.
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.
Find the square root of 169: √169. Choose the correct answer from below.
-13
84.5
13, -13
13
-13
84.5
13, -13
13
The correct answer is 13.
Find the cube root of -729: ∛-729. Choose the correct answer from below:
9, -9
-9
243
9
9, -9
-9
243
9
The correct answer is -9.
Find the cube root of -8: ∛-8.
The cube root of -8 is -2.
What is the irrational square root √63 rewritten as the product of an integer and another irrational square root, in simplest form?
√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.
Therefore, the irrational square root √63 can be rewritten as the product of an integer, 3, and another irrational square root, √7.
What is the irrational cube root ∛81 rewritten as the product of an integer and another irrational cube root?
∛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.
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.
Find the cubic root of 135: ∛135. Choose the correct answer from below:
3∛5
3√5
5∛27
∛5
3∛5
3√5
5∛27
∛5
The cubic root of 135 is 5∛3.
Choose one from the question though
Apologies for the oversight. The correct answer is 3∛5.
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
63.59 miles
14.2 miles
7.07 miles
1413 miles
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.
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.
What is the irrational cube root ∛189 rewritten as the product of an integer and another irrational cube root? Please show your work.
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.
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.
1 answer