How to Multiply Radical Expressions

How to Multiply Radical Expressions

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Multiplying Radical Expressions

To multiply two square roots, radicands should be multiplied together and then write the result under a single radical. Sometimes it could be necessary to further simplify the radical expression. This procedure always stays the same, regardless of the index's value.

Steps of Multiplying Radical Expressions

  • First, the numbers and expressions outside of the radicals should be multiplied.
  • Then, the numbers and expressions inside of the radicals should be multiplied.
  • If necessary, simplify.

Example1

Find the answer: 3 7×5 14

Solution:

  • The numbers and expressions outside and inside of the radicals should be multiplied:
    3 7×5 14 = 3×5 7×14 = 15 98
  • Simplifying:
    15 98 = 15×7 2 = 105 2

Example2

Find the answer: 2 330×3 312

Solution:

  • The numbers and expressions outside and inside of the radicals should be multiplied:
    2 330×3 312 = 2×3 330×12 = 6 3360
  • Simplifying:
    6 3360 = 6 345×8 = 6×2 345 = 12 345

Free printable Worksheets

Exercises for Multiplying Radical Expressions

1) Find the answer: 5 n3×5 n =

2) Find the answer: 35 p7×14 p3 =

3) Find the answer: 48 m10×9 m5 =

4) Find the answer: 30 r9×24 r2 =

5) Find the answer: 14 m11×7 m7 =

6) Find the answer: 18 x18×27 x11 =

7) Find the answer: 12 z16×8 z6 =

8) Find the answer: 21 x10 y2×63 x3 y7 =

9) Find the answer: 66 q9 p7×22 q7 p8 =

10) Find the answer: 17 t5 r6×51 t3 r2 =

 

1) Find the answer: 5 n3×5 n =

5 n3×5 n = 52 n4 = 5 n2

2) Find the answer: 35 p7×14 p3 =

35 p7×14 p3 = 5×7 p7×2×7 p3  = 5×72×2 p2×5 = 7 p5 5×2 = 7 p5 10

3) Find the answer: 48 m10×9 m5 =

48 m10×9 m5 = 3×42 m10×32×m5 = 33×42 m2×7×m = 3×4 m7 3×m =12 m7 3 m

4) Find the answer: 30 r9×24 r2 =

30 r9×24 r2 = 5×3×2 r9×23×3 r2 = 5×32×24 r2×5×r  = 7 p5 5×r= 3×22 r5 10 = 12 r5 10

5) Find the answer: 14 m11×7 m7 =

14 m11×7 m7 = 2×72 m18 = 7 m9 2

6) Find the answer: 18 x18×27 x11 =

18 x18×27 x11 = 2×32 x18×33 x11 = 2×35 x28×x  = 32 x14 2×3×x= 9 x14 6x

7) Find the answer: 12 z16×8 z6 =

12 z16×8 z6 = 3×25 z22 = 4 z11 6

8) Find the answer: 21 x10 y2×63 x3 y7 =

21 x10 y2×63 x3 y7 = 33×72 x13 y9 = 3×7 x6 y4 3 x y = 21 x6 y4 3 x y

9) Find the answer: 66 q9 p7×22 q7 p8 =

66 q9 p7×22 q7 p8 = 2×3×112 q16 p15 = 11 q8 p7 2×3 p = 11 q8 p7 6 p

10) Find the answer: 17 t5 r6×51 t3 r2 =

17 t5 r6×51 t3 r2 = 3×172 t8 r8 = 17 t4 r4 3

Multiplying Radical Expressions Practice Quiz