what is the simplest form of root 200 - root 50
Answers
Answer:
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Concept
The factor of a number that, when multiplied by itself, yields the original number is known as the square root of the number. Special exponents include squares and square roots. Think of the number 9. 3 produces the result 9 when multiplied by itself. This can be expressed as 3² or as 3 x 3. We refer to this as a square since the exponent is 2. The square root of the number is what is meant when the exponent is 1/2. An illustration is √n = n¹/², where n is a positive integer.
Given
√200 ₋ √50
Find
The simplest version of the provided expression is what we are required to determine.
Solution
given, √200 ₋ √50
= √ 2×100 ₋√2 × 25
square of 10 is 100 whereas square of 5 is 25.
so the expression can be written as:
= √2×10² ₋ √2×5²
When square and square root are cancelled, we obtain:
= 10√2 ₋ 5√2
take out the common term √2.
= √2(10 ₋ 5)
= √2(5)
= 5√2
hence we get the simplest form of the given expression as 5√2.
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