Simplifying the Square Root of 20
We can simplify √20 by factoring the number under the root, in this case, 20.
Prime factorisation of 20 yields:
20 = 2 x 2 x 5 = 22 x 5
As you can see, 20 is not a perfect square because we cannot pair the digit 5 after factoring 20. We can only take 22 out of the root.
So, if we take the roots on both sides, we get:
√20 = √(2 x 2 x 5)
Since we only have one pair of numbers (2), taking it outside the root gives us:
√20 = 2√5
From the square root table, we know √5 = 2.236
Therefore:
√20 = 2 x 2.236
√20 = 4.472
Long Division Method
We've just calculated the value of the square root of 20 using prime factorisation. However, since 20 is not a perfect square, we need to remember the √5 value to find the exact value of √20. The long division method allows us to calculate the precise value of √20. Here is a step-by-step solution to evaluate √20:
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