Question

Rút gọn biểu thức:

a) \(A=\sqrt{40^2-24^2}\);                       b) \(B=\left(\sqrt{12}+2\sqrt{3}-\sqrt{27}\right).\sqrt{3}\);

c) \(C=\dfrac{\sqrt{63^3+1}}{\sqrt{63^2-62}}\);                        d) \(D=\sqrt{60}-5\sqrt{\dfrac{3}{5}}-3\sqrt{\dfrac{5}{3}}\).

Answer 1

a: \(A=\sqrt{40^2-24^2}=\sqrt{\left(40-24\right)\left(40+24\right)}\)

\(=\sqrt{16\cdot64}=4\cdot8=32\)

b: \(B=\left(\sqrt{12}+2\sqrt{3}-\sqrt{27}\right)\cdot\sqrt{3}\)

\(=\left(2\sqrt{3}+2\sqrt{3}-3\sqrt{3}\right)\cdot\sqrt{3}\)

\(=\sqrt{3}\cdot\sqrt{3}=3\)

c: \(C=\dfrac{\sqrt{63^3+1}}{\sqrt{63^2-62}}=\dfrac{\sqrt{\left(63+1\right)\left(63^2-63\cdot1+1\right)}}{\sqrt{63^2-62}}\)

\(=\sqrt{\dfrac{64\cdot\left(63^2-63+1\right)}{63^2-62}}=\sqrt{64}\cdot\sqrt{\dfrac{63^2-62}{63^2-62}}\)

\(=\sqrt{64}=8\)

d: \(D=\sqrt{60}-5\sqrt{\dfrac{3}{5}}-3\sqrt{\dfrac{5}{3}}\)

\(=2\sqrt{15}-5\cdot\dfrac{\sqrt{3}}{\sqrt{5}}-3\cdot\dfrac{\sqrt{5}}{\sqrt{3}}\)

\(=2\sqrt{15}-\sqrt{15}-\sqrt{15}=0\)