What is the irrational square root √63 rewritten as the product of an integer and another irrational square root, in simplest form? (1 point)

To rewrite the irrational square root \( \sqrt{63} \) as the product of an integer and another irrational square root, we start by factoring \( 63 \).

We can express \( 63 \) as follows:

\[ 63 = 9 \times 7 \]

Now, we can take the square root of each factor:

\[ \sqrt{63} = \sqrt{9 \times 7} = \sqrt{9} \times \sqrt{7} \]

Since \( \sqrt{9} = 3 \), we have:

\[ \sqrt{63} = 3 \times \sqrt{7} \]

Thus, \( \sqrt{63} \) can be rewritten in simplest form as:

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

What is the irrational square root √63 rewritten as the product of an integer and another irrational square root, in simplest form? (1 point)
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The irrational square root \( \sqrt{63} \) can be rewritten as the product of an integer and another irrational square root by recognizing that:

\[ 63 = 9 \times 7 \]

Taking the square root, we find:

\[ \sqrt{63} = \sqrt{9 \times 7} = \sqrt{9} \times \sqrt{7} \]

Since \( \sqrt{9} = 3 \), we have:

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

Therefore, in simplest form, \( \sqrt{63} \) can be expressed as:

\[ \boxed{3\sqrt{7}} \]

how would you write a number above √

To write a number above the square root symbol (√), you can use a mathematical notation called "radical notation." However, if you're specifically looking to represent this in text form, you might typically write it in LaTeX or in a word processor that supports mathematical formatting. Here are a few ways to represent it:

1. LaTeX Notation: In LaTeX, you can use the following code:

   \sqrt{n}
   

   If you want to display a number above the square root, you might write it like this (using fractions or additional formatting):

   \sqrt{\underline{n}}
   

2. Microsoft Word: In Word, you can use the Equation Editor:

   • Go to "Insert" > "Equation" and then use the square root symbol. You can place a number or expression above the radical symbol by using the "Fraction" tools.

3. Plain Text Representation: If you are limited to plain text, you might denote it by positioning it adjacent to the square root:

   • For example, you could write "√n (number above: m)" to imply that 'm' is considered above the root.

4. HTML: If you are using HTML, you can use superscript for a more visual representation:

   √<sup>n</sup>
   

If you meant writing a number within the radical itself or indicating an expression under the square root (like \( \sqrt{n} \) as "n"), please clarify!

what is the irrational cube root 3√81 rewritten as a product of an integer and another irrational cube root?

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To rewrite the irrational cube root \( \sqrt[3]{81} \) as a product of an integer and another irrational cube root, we will first factor \( 81 \).

The prime factorization of \( 81 \) is: \[ 81 = 3^4 \]

Now we can express \( \sqrt[3]{81} \) as: \[ \sqrt[3]{81} = \sqrt[3]{3^4} \]

We can separate \( 3^4 \) into \( 3^3 \) and \( 3^1 \): \[ \sqrt[3]{81} = \sqrt[3]{3^3 \cdot 3^1} = \sqrt[3]{3^3} \cdot \sqrt[3]{3^1} \]

Since \( \sqrt[3]{3^3} = 3 \), we can simplify this to: \[ \sqrt[3]{81} = 3 \cdot \sqrt[3]{3} \]

Thus, in simplest form, \( \sqrt[3]{81} \) can be expressed as: \[ \boxed{3\sqrt[3]{3}} \]

Find the square root of 169: √169

The square root of \( 169 \) is calculated as follows:

\[ \sqrt{169} = 13 \]

Thus, the result is:

\[ \boxed{13} \]