Solutions — Surds 4C Worksheet
Year 10 Mathematics Core · Cambridge Ch 4, §4C · Mr Wong
ANSWER KEY
Warm-up
Q1. Missing parts (fill the gaps):
a $\sqrt{15\div 3}=\sqrt{5}$
b $\sqrt{42\div 7}=\sqrt{6}$
c $\sqrt{6\times 5}=\sqrt{30}$
d $\sqrt{11\times 2}=\sqrt{22}$
Q2. Squares of surds:
Part A — Multiplying surds
Q3. Multiply and simplify:
a $\sqrt{21}$
b $2\sqrt{5}$ ($\sqrt{20}=\sqrt{4\cdot 5}$)
c $4\sqrt{10}$
d $15\sqrt{6}$
e $20\sqrt{3}$ ($10\sqrt{12}=10\cdot 2\sqrt{3}$)
f $30\sqrt{2}$ ($6\sqrt{50}=6\cdot 5\sqrt{2}$)
Q4. Squares of surds (whole-number answers):
a $6$
b $11$
c $18$ ($9\times 2$)
d $80$ ($16\times 5$)
Part B — Dividing surds
Q5. Divide and simplify:
a $2$ ($\sqrt{4}$)
b $\sqrt{5}$
c $3$ ($\sqrt{9}$)
d $4$ ($2\sqrt{4}$)
e $12$ ($4\sqrt{9}$)
f $10$ ($2\sqrt{25}$)
Part C — Distributive law
Q6. Expand and simplify:
a $\sqrt{10}+\sqrt{14}$
b $6-\sqrt{15}$ ($\sqrt{3}\cdot 2\sqrt{3}=6$)
c $10\sqrt{2}+30$ ($2\sqrt{50}+6\cdot 5$)
d $2\sqrt{3}+3\sqrt{2}$ ($\sqrt{12}+\sqrt{18}$)
Challenge
Q7. Rectangle with length $3\sqrt{6}$ cm and width $2\sqrt{2}$ cm:
a
Area $= 3\sqrt{6}\times 2\sqrt{2}=6\sqrt{12}=$ $12\sqrt{3}\;\text{cm}^2$
b
Perimeter $= 2(3\sqrt{6}+2\sqrt{2})=$ $6\sqrt{6}+4\sqrt{2}\;\text{cm}$
c
Diagonal $d^{2}=(3\sqrt{6})^{2}+(2\sqrt{2})^{2}=54+8=62$, so $d=\sqrt{62}\;\text{cm}$
Q8. $\big(3\sqrt{2}+\sqrt{5}\big)\big(3\sqrt{2}-\sqrt{5}\big)$:
·
Difference of squares: $(3\sqrt{2})^{2}-(\sqrt{5})^{2}=18-5=$ $13$ (a whole number ✓)