Question concerning simplification of numerical expression with square roots.

In summary, to simplify a numerical expression with square roots, you need to find the perfect square factors of the number inside the square root and multiply them together. A perfect square factor is a number that can be multiplied by itself to get a whole number. You cannot simplify a numerical expression with square roots if the number inside the square root is negative. Simplifying involves factoring out perfect square factors, while evaluating involves finding the numerical value. There are rules and guidelines to follow, such as factoring and following the order of operations.
  • #1
shamieh
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0
how does \(\displaystyle \frac{5700}{\sqrt{15,300}}\) turn into \(\displaystyle \frac{570}{\sqrt{153}}\) ??
 
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  • #2
shamieh said:
how does \(\displaystyle \frac{5700}{\sqrt{15,300}}\) turn into \(\displaystyle \frac{570}{\sqrt{153}}\) ??

$$\frac{5700}{\sqrt{15,300}}=\frac{5700}{\sqrt{153 \cdot 100}}
=\frac{5700}{\sqrt{153} \sqrt{100}}=\frac{5700}{10\sqrt{153}}
=\frac{570}{\sqrt{153}}.$$
 

FAQ: Question concerning simplification of numerical expression with square roots.

How do you simplify a numerical expression with square roots?

To simplify a numerical expression with square roots, you need to find the perfect square factors of the number inside the square root. Then, you can take the square root of each perfect square factor and multiply them together. Finally, you can simplify any remaining square roots if possible.

What is a perfect square factor?

A perfect square factor is a number that can be multiplied by itself to get a whole number. For example, the perfect square factors of 36 are 1, 4, 9, and 36.

Can you simplify a numerical expression with square roots if the number inside the square root is negative?

No, you cannot simplify a numerical expression with square roots if the number inside the square root is negative. This is because the square root of a negative number is not a real number.

What is the difference between simplifying and evaluating a numerical expression with square roots?

Simplifying a numerical expression with square roots involves simplifying the expression to its simplest form by factoring out perfect square factors. Evaluating a numerical expression with square roots involves finding the actual numerical value of the expression, usually by substituting a number in for the variable.

Are there any rules or guidelines for simplifying numerical expressions with square roots?

Yes, there are a few rules and guidelines to follow when simplifying numerical expressions with square roots. These include factoring out perfect square factors, simplifying any remaining square roots if possible, and following the order of operations.

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