Question

a)(radical27-4)(3radical3+4)
b)(radical2+1)²+2radical8
c)(radical5-2)²+4(radical5-1)

Answer 1

$a)( \sqrt{27} - 4)(3 \sqrt{3} + 4)$

$= (3 \sqrt{3} - 4)(3 \sqrt{3} + 4)$

$= {(3 \sqrt{3}) }^{2} - {4}^{2}$

$= 27 - 16$

$= 11$

$b) {( \sqrt{2} + 1) }^{2} + 2 \sqrt{8}$

$= {( \sqrt{2}) }^{2} + 2 \times \sqrt{2} \times 1 + {1}^{2}+2 \times 2 \sqrt{2}$

$= 2 + 2 \sqrt{2} +1 + 4 \sqrt{2}$

$= 6 \sqrt{2} + 3$

$= 3(2 \sqrt{2} + 1)$

$c) {( \sqrt{5} - 2)}^{2} + 4( \sqrt{5} - 1)$

$= {( \sqrt{5}) }^{2} - 2 \times \sqrt{5} \times 2 + {2}^{2} + 4 \sqrt{5} - 4$

$= 5 - 4 \sqrt{5} + 4 + 4 \sqrt{5} - 4$

$= 5 + 4 \sqrt{5} - 4 \sqrt{5} + 4 - 4$

$= 5$