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From the definition it is evident that a radical is an incommensurable quantity, although its value can be determined to any degree of accuracy should not be noted that quantities √4, (27) ^ (1/3), (16 / 81) ^ (1/4) etc., expressed in the form radical are commensurable quantities are not radical because

In fact, any root of an algebraic expression regarded as a radical.

√32 – 2 √18 + 5 √2 + 2 ^ (3/2)= √(16 * 2) – 2 √(9*2) + 5 √2 +√(2^3)

=4√2 - 6√2 +5√2+2√2

=(4-6+5+2) √2

=5√2

Answer: - 5√2

3√2 x 5 (4) ^(1/3) x 4 (8)^(1/4) = (3x5x4)x[2^(1/2) x 4^(1/3) x 8^(1/4)]

= 60 x 2^ (1/2) x 2^(2/3) x 2^(3/4)

= 60 x 2^ (1/2 + 2/3 + ¾)

= 60 x 2^ (23/12)

= 60 x (2^23) ^(1/12)

=60 x [2^ (12+11)] ^(1/12)

= 60 x (2^12 x 2^11)^(1/12)

= 60 x 2 x(2^11)^(1/12)

= 120 x (2048)^ (1/2)

= 120 (2048)^(1/2)