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The rationalization of the denominator of $10 − 5 2$ is equal to ____.

Use $2 = 1.414, 3 = 1.732 and 5 = 2.236$

(Upto three decimal places)

see full answer

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Detailed Solution

The rationalization of the denominator of

10 − 5 2

is equal to 0.463.
It is given that the mathematical expression is

10 − 5 2

2 = 1.414

3 = 1.732 and 5 = 2.236

.
Let

E = 10 − 5 2

We know that

10 = 2 ⋅ 5

. Substituting the above in the given mathematical expression,

E = 10 − 5 2 = 52 − 5 2 = 5 2 − 1 2 = 2.236 1.414 − 1 2 = 1.118 × 0.414 = 0.46285 = 0.463

Hence, the rationalization of the denominator of

10 − 5 2

is equal to 0.463.

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