Number - Surds

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Question 1


Evaluate

a) $\sqrt9$a s v d
b) $\sqrt{25}$a s v d
c) $\sqrt{49}$a s v d
d) $\sqrt{121}$a s v d
e) $\sqrt{4}$a s v d
f) $\sqrt{64}$a s v d
g) $\sqrt{144}$a s v d
h) $\sqrt{1}$a s v d


Question 2


Type the following into a calculator and round to $2$ decimal places.

a) $\sqrt3$a s v d
b) $\sqrt5$a s v d
c) $\sqrt{10}$a s v d
d) $\sqrt{19}$a s v d
e) $\sqrt{20}$a s v d
f) $\sqrt{2}$a s v d
g) $\sqrt{11}$a s v d
h) $\sqrt{26}$a s v d


Question 3


Simplify

a) $\left(\sqrt9\right)^2$a s v d
b) $\left(\sqrt{25}\right)^2$a s v d
c) $\left(\sqrt{5}\right)^2$a s v d
d) $\left(\sqrt{2}\right)^2$a s v d
e) $\left(\sqrt{19}\right)^2$a s v d
f) $\left(\sqrt{100}\right)^2$a s v d
g) $\left(\sqrt{115}\right)^2$a s v d
h) $\left(\sqrt{738}\right)^2$a s v d


Question 4


Classify the following as rational or irrational numbers

a) $5$a s v d
b) $\frac12$a s v d
c) $0.7$a s v d
d) $0.\dot3$a s v d
e) $0.9384759287583...$a s v d
f) $\sqrt3$a s v d
g) $0.\dot1\dot3$a s v d
h) $\sqrt{18}$a s v d


Question 5


Classify the following as surds or a rational number

a) $\sqrt3$a s v d
b) $\sqrt7$a s v d
c) $3$a s v d
d) $\sqrt9$a s v d
e) $\sqrt{\frac{4}{9}}$a s v d
f) $\sqrt{\frac{5}{9}}$a s v d
g) $\sqrt{0.1}$a s v d
h) $\sqrt{0.16}$a s v d


Question 6


Simplify

a) $\left(\sqrt3\right)^4$a s v d
b) $\left(\sqrt5\right)^4$a s v d
c) $\left(\sqrt{9}\right)^4$a s v d
d) $\left(\sqrt{2}\right)^6$a s v d
e) $\left(\sqrt{3}\right)^6$a s v d
f) $\left(\sqrt{2}\right)^8$a s v d
g) $\left(\sqrt{16}\right)^3$a s v d
h) $\left(\sqrt{25}\right)^3$a s v d


Question 7


Evaluate

a) $2\times\sqrt3$a s v d
b) $3\times\sqrt7$a s v d
c) $4\times2\sqrt5$a s v d
d) $8\times3\sqrt{10}$a s v d
e) $5\times5\sqrt{21}$a s v d
f) $3\times\sqrt{25}$a s v d
g) $2\sqrt{36}$a s v d
h) $8\times3\sqrt{64}$a s v d


Question 8


Evaluate

a) $\sqrt2\times\sqrt2$a s v d
b) $\sqrt7\times\sqrt7$a s v d
c) $\sqrt9\times\sqrt9$a s v d
d) $\sqrt{42}\times\sqrt{42}$a s v d
e) $\sqrt{5}\times\sqrt5\times\sqrt5$a s v d
f) $\sqrt2\times\sqrt2\times\sqrt2$a s v d
g) $\sqrt{16}\times\sqrt{16}\times\sqrt{16}$a s v d
h) $3\times\sqrt{11}\times\sqrt{11}\times\sqrt{11}$a s v d


Question 9


Simplify

a) $\sqrt3+\sqrt3$a s v d
b) $\sqrt6+\sqrt6$a s v d
c) $\sqrt5+\sqrt5+\sqrt5$a s v d
d) $\sqrt{11}+\sqrt{11}+\sqrt{11}+\sqrt{11}$a s v d
e) $2\sqrt{13}+\sqrt{13}$a s v d
f) $3\sqrt{22}+2\sqrt{22}$a s v d
g) $5\sqrt{7}+3\times\sqrt{7}$a s v d
h) $13\times\sqrt{39}+2\times\sqrt{39}+\sqrt{39}$a s v d


Question 10


Simplify

a) $2\sqrt3-\sqrt3$a s v d
b) $5\sqrt{15}-\sqrt{15}$a s v d
c) $10\sqrt{21}-2\sqrt{21}$a s v d
d) $15\sqrt{15}-5\times\sqrt{15}$a s v d
e) $11\times\sqrt{43}-11\sqrt{43}$a s v d
f) $92\times\sqrt{94}-100\sqrt{94}$a s v d
g) $22\sqrt4-10\times\sqrt4$a s v d
h) $\sqrt{14}-2\sqrt{14}-33\times\sqrt{14}$a s v d


Question 11


Simplify

a) $\sqrt3\times\sqrt3+\sqrt5$a s v d
b) $\left(\sqrt{19}\right)^2+\sqrt{19}$a s v d
c) $\left(\sqrt{7}\right)^2+\left(\sqrt{7}\right)^4$a s v d
d) $\left(\sqrt{3}\right)^3$a s v d
e) $\left(\sqrt{11}\right)^3$a s v d
f) $\left(\sqrt{2}\right)^5$a s v d
g) $\sqrt6\times5\times\sqrt6\times3$a s v d
h) $\left(\sqrt{10}\right)^2\times5\times\sqrt{10}\times\sqrt9$a s v d