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Which equations support the fact that rational numbers are closed under subtraction?

select all that apply

Asquare root of 8 - square root of 8 = 0

b.4.5-0.5=4

c.5square root of 4 - square root of 4 = 4 square root of 4

d.2 square root of 3 - square root of 3 = square root of 3

Verified Answer :

Rational number are said to be closed under subtraction if,

Subtraction of two rational number results in a rational number.

Suppose a and b are two rational number , if

a - b = A rational number.

It means rational number satisfies closure property under subtraction.

For example, a = 5, b= 3

Then, a-b or b-a is a rational number i.e 2 or -2.Hence the result is a rational number.

Out of the given options

4.5 - 0.5 =0, As 4.5 =20, 0.5=0, 20 and 0 are rational number. 20 -0=20, but RHS=4 is not equal to LHS.It is closed under subtraction, but LHS = RHS.So this can't be the result.

Option (c) which is 5√4 -√4 = 4√4, as 5√4= 5×2=10, √4=2 and 10-2=8=L H S  and R H S = 4√4=4 × 2 = 8,which shows that L H S= R HS

Hence Option (C) is the desired result.

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