Question

Simplify the following​

Answer 1

Step-by-step explanation:

please I solved the question in the diagram above

Answer 2

Answer:

1) 11$\sqrt{3}$

2) 2$\sqrt{2}$

3) $20\sqrt{3} + 15\sqrt{2}$

4) $53 + 12\sqrt{10}$

5) -2

6) $7\sqrt{2} - 5\sqrt{3}$

Step-by-step explanation:

1) 2$\sqrt{12}$ + 3$\sqrt{48}$ - $\sqrt{75}$

=(2 × 2$\sqrt{3}$ )+ (3 × 4$\sqrt{3}$) - 5$\sqrt{3}$

= 4$\sqrt{3}$ + 12$\sqrt{3}$ - 5$\sqrt{3}$

= 11$\sqrt{3}$

2) 4$\sqrt{8}$ -2$\sqrt{98}$ + $\sqrt{128}$

= (4 × 2$\sqrt{2}$) - (2 × 7$\sqrt{2}$) + 8$\sqrt{2}$

= 8$\sqrt{2}$ - 14$\sqrt{2}$ +8$\sqrt{2}$

= 2$\sqrt{2}$

3) 5$\sqrt{12\\}$ - 3$\sqrt{18} + 4 \sqrt{72} +2\sqrt{75}$

= 5× $2\sqrt{3}$ - 3×$3\sqrt{2}$ + 4×$6\sqrt{2}$ + 2×$5\sqrt{3}$

= $10\sqrt{3} - 9\sqrt{2} +24\sqrt{2} +10\sqrt{3}$

= $20\sqrt{3} + 15\sqrt{2}$

4) $(2\sqrt{2} + 3\sqrt{5} )^{2}$

= $8 + 12\sqrt{10} + 45$

= $53 + 12\sqrt{10}$

5) $(1+\sqrt{3} ) (1-\sqrt{3} )$

= $1 - 3$

= -2

6) $(2\sqrt{6} -1) (\sqrt{3} -\sqrt{2} )$

= $2\sqrt{18}-2\sqrt{12} -\sqrt{3} +\sqrt{2}$

= 2×$3\sqrt{2}$ - 2×$2\sqrt{3}$ - $\sqrt{3} + \sqrt{2}$

= $6\sqrt{2} - 4\sqrt{3} -\sqrt{3} +\sqrt{2}$

= $7\sqrt{2} - 5\sqrt{3}$

Hope the working out is clear and will help you. :)