Đáp án:
Giải thích các bước giải:
a. A = $\sqrt[]{4+\sqrt[]{7}}$ - $\sqrt[]{4-\sqrt[]{7}}$
⇒ $\sqrt[]{2}$A = $\sqrt[]{8+2\sqrt[]{7}}$ - $\sqrt[]{8-2\sqrt[]{7}}$
⇔ $\sqrt[]{2}$A = $\sqrt[]{(\sqrt[]{7}+1)²}$ - $\sqrt[]{(\sqrt[]{7}-1)²}$
⇔ $\sqrt[]{2}$A = $\sqrt[]{7}$ + 1 - $\sqrt[]{7}$ + 1 = 2
⇒ A = $\sqrt[]{2}$
b. B = $\sqrt[]{6+2\sqrt[]{2}×\sqrt[]{3-\sqrt[]{4+2\sqrt[]{3}}}}$
B = $\sqrt[]{6+2\sqrt[]{2}×\sqrt[]{3-\sqrt[]{(\sqrt[]{3}+1)²}}}$
B = $\sqrt[]{6+2\sqrt[]{2}×\sqrt[]{3-\sqrt[]{3}-1}}$
B = $\sqrt[]{6+2\sqrt[]{2}×\sqrt[]{2-\sqrt[]{3}}}$
B = $\sqrt[]{6+2×\sqrt[]{4-2\sqrt[]{3}}}$
B = $\sqrt[]{6+2×\sqrt[]{(\sqrt[]{3}-1)²}}$
B = $\sqrt[]{6+2×(\sqrt[]{3}-1)}$
B = $\sqrt[]{4+2×\sqrt[]{3}}$
B = $\sqrt[]{(\sqrt[]{3}+1)²}$ = $\sqrt[]{3}$ + 1
c. C = $\sqrt[]{3-\sqrt[]{5}}$×( $\sqrt[]{3}$ - $\sqrt[]{3}$ )×( 3 + $\sqrt[]{5}$ )
C = $\sqrt[]{3-\sqrt[]{5}}$×( 3$\sqrt[]{10}$ + $\sqrt[]{50}$ - 3$\sqrt[]{2}$ - $\sqrt[]{10}$ )
C = $\sqrt[]{3-\sqrt[]{5}}$×( 2$\sqrt[]{10}$ + 5$\sqrt[]{2}$ - 3$\sqrt[]{2}$ )
C = $\sqrt[]{3-\sqrt[]{5}}$×( 2$\sqrt[]{10}$ + 2$\sqrt[]{2}$ )
C = $\sqrt[]{6-2\sqrt[]{5}}$×( 2$\sqrt[]{5}$ + 2 )
C = 2×$\sqrt[]{(\sqrt[]{5}-1)²}$×( $\sqrt[]{5}$ + 1 )
C = 2×( $\sqrt[]{5} -1$ )×( $\sqrt[]{5}$ + 1 )
C = 2×( 5 - 1 ) = 8
