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Gyaan Maths
CBSE · Class 6-12
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Class 8 · Ganita Prakash
Unit 1 · Class 8Ganita Prakash
A Square and A Cube
Squares, square roots, cubes, and cube roots.
Lessons
4 concepts
1
Squares & Patterns
Square numbers:
1
,
4
,
9
,
16
,
…
1, 4, 9, 16, \ldots
1
,
4
,
9
,
16
,
…
. Sum of first
n
n
n
odd numbers
=
n
2
= n^2
=
n
2
.
(
n
+
1
)
2
−
n
2
=
2
n
+
1
(n+1)^2 - n^2 = 2n+1
(
n
+
1
)
2
−
n
2
=
2
n
+
1
.
2
Square Roots by Factorisation
144
\sqrt{144}
144
: factorise
144
=
2
4
⋅
3
2
144 = 2^4\cdot 3^2
144
=
2
4
⋅
3
2
. Pair the primes:
(
2
2
)
(
3
)
=
12
(2^2)(3) = 12
(
2
2
)
(
3
)
=
12
.
3
Cubes
Cubes:
1
,
8
,
27
,
64
,
…
1, 8, 27, 64, \ldots
1
,
8
,
27
,
64
,
…
. Cube of a negative is negative.
(
−
3
)
3
=
−
27
(-3)^3 = -27
(
−
3
)
3
=
−
27
.
4
Cube Roots by Factorisation
216
3
\sqrt[3]{216}
3
216
:
216
=
2
3
⋅
3
3
216 = 2^3\cdot 3^3
216
=
2
3
⋅
3
3
; triple →
(
2
)
(
3
)
=
6
(2)(3) = 6
(
2
)
(
3
)
=
6
.
Skills to practise
Skill · medium
A Square and A Cube — Practice