Multiply (519 −−−√ ) (62–√) . Give an exact answer
To multiply the expression (519 −−−√ ) (62–√), we first simplify the square roots:
√519 = 57.23 (approximated to two decimal places), since 57.23 × 57.23 ≈ 519.
√62 = 7.87 (approximated to two decimal places), since 7.87 × 7.87 ≈ 62.
Now, we can multiply the two simplified expressions:
(519 −−−√ ) (62–√) = 57.23 × 7.87
= 450.9101 (approximated to four decimal places)
Therefore, the exact answer is 450.9101.
Question
Divide 95√35√ . Provide an exact answer. (1 point)
To divide √95 by √35, we can simplify both square roots:
√95 = √(19 × 5) = √19 √5
Similarly,
√35 = √(7 × 5) = √7 √5
Now, we can simplify the division:
(√19 √5) / (√7 √5) = (√19 / √7) * (√5 / √5) = (√19 / √7) * 1 = √19 / √7
Therefore, the exact answer to the expression √95 / √35 is √19 / √7.
Divide 3639√913√ . Provide an exact answer. (1 point)
To divide √3639 by √913, we can simplify both square roots:
√3639 = √(121 × 30) = 11 √30
Similarly,
√913 = √(121 × 7) = 11 √7
Now, we can simplify the division:
(11 √30) / (11 √7) = (11 / 11) * (√30 / √7) = √30 / √7
Therefore, the exact answer to the expression √3639 / √913 is √30 / √7.
What is the irrational square root 63−−√ rewritten as the product of an integer and another irrational square root, in simplest form?
To rewrite the irrational square root of 63 ( √63 ) as the product of an integer and another irrational square root, we need to find a perfect square factor of 63.
The prime factorization of 63 is 3 × 3 × 7.
We can rewrite this as:
√(3 × 3 × 7) = √(3^2 × 7) = √(9 × 7) = √63
Now, we can simplify this further:
√(9 × 7) = √9 × √7 = 3 √7
Therefore, the irrational square root of 63 ( √63 ) can be rewritten as the product of an integer (3) and another irrational square root (√7), in simplest form.
What is the irrational cube root 81−−√3 rewritten as a product of an integer and another irrational cube root?
To rewrite the irrational cube root of 81 ( ∛81 ) as a product of an integer and another irrational cube root, we need to find a perfect cube factor of 81.
Since 81 itself is a perfect cube (3^4), we can rewrite this as:
∛(3^4 × 3) = ∛(3^5) = ∛243
Now, we can simplify this further:
∛243 = ∛(3^5) = 3 ∛3
Therefore, the irrational cube root of 81 ( ∛81 ) can be rewritten as the product of an integer (3) and another irrational cube root (∛3), in simplest form.
Find the square root of 169: 169−−−√.(1 point)
Responses
84.5
84.5
−13
negative 13
13,−13
13 comma negative 13
13