!
Surds
Videos 305, 306, 307, 308 on Corbettmaths
Workout
Question 1: Work out each of the following
(a) √3 ╳ √5 (b) √7 ╳ √2 (c) √11 ╳ √6 (d) √2 ╳ √3 (e) √8 ╳ √2 (f) √3 ╳ √3 (g) √5 ╳ √6 (h) √5 ╳ √2 (i) √6 ╳ √6 (j) √10 ╳ √3 (k) √5 ╳ √20 (l) √11 ╳ √10 (m) √2 ╳ √5 ╳ √3 (n) √2 ╳ √6 ╳ √3 (o) √10 ╳ √7 ╳ √3
(p) √2 ╳ √2 ╳ √2 (q) √2 ╳ √3 ╳ √2 ╳ √3
Question 2: Work out each of the following
(a) (√3)² (b) (√7)² (c) (√10)² (d) (√5)²
Question 3: Work out each of the following
(a) (√2)³ (b) (√6)³ (c) (√10)³ (d) (√3)³
(e) (√3)⁴ (f) (√5)⁴ (g) (√10)⁴ (h) (√2)⁵
Question 4: Work out each of the following
(a) 2√3 ╳ 3√5 (b) 7√2 ╳ 4√11 (c) 2√13 ╳ 2√2 (d) 10√2 ╳ 5√3
(e) √3 ╳ 6√5 (f) 2√2 ╳ √7 (g) 4√3 ╳ 2√3 (h) 2√2 ╳ 3√8
(i) 2√2 ╳ √5 ╳ 4√3 (j) 3√2 ╳ 2√6 ╳ 2√3 Question 5: Work out each of the following
(a) √10 ÷ √5 (b) √21 ÷ √7 (c) √30 ÷ √6 (d) √8 ÷ √2 (e) √80 ÷ √5 (f) √56 ÷ √7 (g) √15 ÷ √3 (h) √72 ÷ √8 (i) √7 ÷ √7 (j) √26 ÷ √13 (k) √48 ÷ √12 (l) √48 ÷ √8
© CORBETTMATHS 2016
!
Surds
Videos 305, 306, 307, 308 on Corbettmaths
Question 6: Work out each of the following
(a) 4√6 ÷ 2√2 (b) 12√10 ÷ 3√5 (c) 9√15 ÷ 3√3 (d) 7√30 ÷ √2
(e) 20√8 ÷ 5√2 (f) 40√80 ÷ 20√5 (g) 51√7 ÷ 3√7 (h) 36√54 ÷ 18√6
Question 7: Work out each of the following
(a) (b) (c) (d)
Question 8: Simplify the following
(a) √8 (b) √75 (c) √20 (d) √32 (e) √48 (f) √200
(g) √300 (h) √80 (i) √50 (j) √98 (k) √63 (l) √800
(m) √180 (n) √220 (o) √96 (p) √175 (q) √1000 (r) √60
(d) 3√98 (e) 15√32 (f) 10√75
Question 9: Simplify the following
(a) 5√8 (b) 2√20 (c) 4√50 Question 10: Work out each of the following. Simplify each answer.
(a) √6 ╳ √10 (b) √15 ╳ √10 (c) √30 ╳ √6
(d) √22 ╳ √10 (e) 3√2 ╳ √6 (f) √14 ╳ 4√2
(g) 4√6 ╳ 3√15 (h) 2√70 ╳ 3√10 (i) 5√10 ╳ 2√30
Question 11: Work out the following additions/subtractions
(a) √8 + √18 (b) √50 + √8 (e) √8 + √2 + √72 (f) √300 − √48 (c) √75 + √27 (d) √200 − √32
(g) √1000 + √90 (h) √28 + √63
Question 12: Work out the following additions/subtractions
(a) 3√8 + √2 (b) 4√27 − √75 (c) 2√50 + 5√32 (e) 4√80 + 3√45 (f) 6√75 − 2√12 (g) 10√7 + 2√175 © CORBETTMATHS 2016
(d) √200 − 3√18
!
Surds
Videos 305, 306, 307, 308 on Corbettmaths
Question 13: Expand each of the following. Simplify if possible.
(a) √2(√3 + 5) (b) √3(√5 + √2) (e) √2(√18 − √2) (f) √5 ( 3√2 − √5) (i) √27 (√2 + √3) (j) √12 (7 − √3) (c) √6 (2 − √3) (d) √10 (5 + √10)
(g) 2√3 (3√2 + √3) (h) 4√11( 5√2 + 2√11)
Question 14: Expand each of the following. Simplify if possible.
(a) (2 + √3)(1 + √3) (b) (√2 + 5)(1 + √2) (c) (√3 + 1)(√3 + 4) (d) (3 + √5)(4 − √5) (e) (√7 − 1)(√7 − 1) (f) (5 − √3)(5 + √3)
(g) (3 + √2)(1 + √3) (h) (√12 + √3)(√3 + 2) (i) (4 − √2)(3 + √8)
(j) (√7 + √2)(√8 + √7) (k) (1 + 2√2)(2 − √2) (l) (3√5 + 7)(2√5 + 1)
(m) (3 + √2)² (n) (1 + √5)² (o) (10 − √2)² (p) (√5 + √2)² (q) (2√3 − 1)² (r) (5√2 + 3√3)² Question 15: Expand each of the following. Simplify if possible.
(a) (4 + √3)(4 − √3) (b) (1 − √6)(1 + √6) (c) (√10 + 1)(√10 − 1) (d) (√7 + √5)(√7 − √5) (e) (2√3 − 1)(2√3 + 1) (f) (5 − 4√3)(5 + 4√3)
Question 16: Rationalise the denominators for each of the following
(a) (b) (c) (d)
(e) (f) (g) (h)
(i) (j) (k) (l)
© CORBETTMATHS 2016
!
Surds
Videos 305, 306, 307, 308 on Corbettmaths
Question 17: Rationalise the denominators for each of the following
(a) (b) (c) (d)
(e) (f) (g) (h)
(c)
Apply
Question 1: Find the area of each of these rectangles
(a) (b) Question 2: Find the perimeter of each of these rectangles
(a) (b) (c)
Question 3: Calculate x for each of the following right angled triangles.
Give your answer as a simpli\ied surd (or integer).
(a) (b) (c) (d)
© CORBETTMATHS 2016
!
Surds
Videos 305, 306, 307, 308 on Corbettmaths
Question 4: A shed has dimensions, in metres, of height √5, width √6 and length √10
Find the volume of the shed. Give your answer as a simpli\ied surd.
Question 5: Mrs Jenkins is making decorations for a wedding.
She needs 18√5 metres of ribbon in total.
Mrs Jenkins has 40 metres of ribbon.
Does she have enough ribbon?
Question 6: The midpoints of the sides of a square of side 16cm are joined to form another square. This process is then repeated to create the shaded square.
Question 7: Find the area of the shaded square.
The area of a rectangle is √125 cm²
The length of the rectangle is (2 + √5) cm.
Calculate the width of the rectangle.
Express your answer in the form a + b√5, where a and b are integers.
Question 8: The triangle below has an area of 2√6 cm².
Find the height of the triangle, x.
Give your answer as a simpli\ied surd.
© CORBETTMATHS 2016