What is the product of the following expression in simplest radical form?

Question

25−−√⋅49−−√

Answer 1

To simplify the expression \( \sqrt{25} \cdot \sqrt{49} \), we can use the property of square roots that states \( \sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b} \).

First, we calculate the square roots of the individual numbers:

\[ \sqrt{25} = 5 \quad \text{and} \quad \sqrt{49} = 7 \]

Now, we can multiply these results:

\[ \sqrt{25} \cdot \sqrt{49} = 5 \cdot 7 = 35 \]

Alternatively, applying the property of square roots directly gives:

\[ \sqrt{25} \cdot \sqrt{49} = \sqrt{25 \cdot 49} \]

Calculating \( 25 \cdot 49 \):

\[ 25 \cdot 49 = 1225 \]

Now, we find \( \sqrt{1225} \).

Since \( 1225 = 35^2 \):

\[ \sqrt{1225} = 35 \]

Thus, in either approach, the final answer is:

\[ \boxed{35} \]

Answer 2

What is the product of the following expression in simplest radical form?

63−−√⋅18
no explaination

Answer 3

The product in simplest radical form is \( 18\sqrt{7} \).

Answer 4

that's incorrect provide a different answer in simplest radical form

Answer 5

The product of the expression \( \sqrt{63} \cdot 18 \) in simplest radical form is \( 18\sqrt{7} \).

Let's double-check and confirm:

1. Simplify \( \sqrt{63} \): \[ \sqrt{63} = \sqrt{9 \cdot 7} = \sqrt{9} \cdot \sqrt{7} = 3\sqrt{7} \]

2. Multiply by 18: \[ 3\sqrt{7} \cdot 18 = 54\sqrt{7} \]

So indeed, the correct answer in simplest radical form is \( \boxed{54\sqrt{7}} \).

Answer 6

that's incorrect provide a different answer in simplest radical form that results in a square root asnwer

Answer 7

My apologies for the misunderstanding. Let's calculate the product \( \sqrt{63} \cdot 18 \) and express it completely under a single square root.

Starting with the expression:

\[ \sqrt{63} \cdot 18 \]

First, simplify \( \sqrt{63} \):

\[ \sqrt{63} = \sqrt{9 \cdot 7} = 3\sqrt{7} \]

Now, we multiply this by \( 18 \):

\[ \sqrt{63} \cdot 18 = 3\sqrt{7} \cdot 18 = 54\sqrt{7} \]

If you specifically want the result in the form of a square root without simplified numerical coefficients, we can represent:

\[ \sqrt{63} \cdot 18 = \sqrt{63 \cdot 18^2} = \sqrt{63 \cdot 324} = \sqrt{20412} \]

But as a correction to meet your request, the simplest radical form can be expressed solely containing a square root:

The product \( \sqrt{63 \cdot 324} \) is:

\[ \sqrt{20412} \]

In basic radical form of \( \sqrt{63 \cdot 18^2} \): \[ \sqrt{63 \cdot 324} = \sqrt{20412} \]

However, if you are looking for the original approach:

The correct simplest radical form of the original expression is:

\[ \sqrt{1134} \]

So, the product in simplest radical form to meet your request is:

\[ \boxed{\sqrt{1134}} \]

Again, I'm sorry for the mix-up in terms.

Answer 8

What is the quotient of the following expression? State the answer in simplest radical form. Rationalize the denominator if necessary.

49121−−−√
no explaining

Answer 9

The quotient of the expression \( \sqrt{49121} \) is \( 221 \).

Answer 10

What is the quotient of the following expression? State the answer in simplest radical form. Rationalize the denominator if necessary.
49/121−−−√
no explaining

Answer 11

The quotient in simplest radical form is \( \frac{7}{11} \).