Give two mixed radicals that are equivalent to \sqrt{500}. Which

Umaiza Hutton

Umaiza Hutton

Answered question

2022-03-01

Give two mixed radicals that are equivalent to 500. Which answer is in simplest radical form? How do you know?

Answer & Explanation

flytandikqk

flytandikqk

Beginner2022-03-02Added 4 answers

Step 1
Think of the ' factorisation
500=22×53
The rules for non-negative numbers are as follows:
a=a12
(ab)=abc
(a×b)c=ac×bc
Thus:
500=253=522×5=105
I think it is obvious which is in lowest form.

Jocelyn Harwood

Jocelyn Harwood

Beginner2022-03-03Added 8 answers

Step 1
Simplifying radicals, in this case a square root, is a matter of finding the largest square root that will divide into 500
In the case of 500, I start with the perfect square greater then 1 and try to find the largest perfect square {1,4,9,16,25,36} that divides 500. Now 4 works (4×125) but is it the largest. How about 25?
It works:
500=25×20
But 20 still divides by 4, which is a perfect square.
By now you may see that 100 is the largest perfect square that divides 500.
500=100×5
Thus, using 100, we have 500=100×5
This uses the property that the square root of a product is equal to the product of the square roots. Thus
500=100×5=105
This is considered fully simplified. There are no other perfect squares, other than 1, that can be factored out of 105
Answer: 105

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