Simplification -
1) √2 × √8
[tex] \sqrt{2 \times 8} \\ [/tex]
[tex] \sqrt{2 \times 2 \times 2 \times 2} [/tex]
[tex] \sqrt{ {2}^{2} \times {2}^{2} } \\ [/tex]
[tex]2 \times 2 = 4[/tex]
→ 4
2) √125 × √5
[tex] \sqrt{5 \times 5 \times 5} \times \sqrt{5} [/tex]
[tex] \sqrt{ {5}^{2} \times 5} \times \sqrt{5} \\ [/tex]
[tex]5 \sqrt{5 \times 5} [/tex]
[tex]5 \times 5 = 25 \\ [/tex]
→ 25
3) √8/√2
[tex] \frac{ \sqrt{2 \times 2 \times 2} }{ \sqrt{2} } \\ [/tex]
[tex] \frac{2 \sqrt{2} }{ \sqrt{2} } \\ [/tex]
[tex] = > 2 \\ [/tex]
4) 16√10/4√2
[tex] \frac{16 \sqrt{5 \times 2} }{4 \sqrt{2} } \\ [/tex]
[tex] \frac{4 \sqrt{5} \sqrt{2} }{ \sqrt{2} } \\ [/tex]
[tex] = > 4 \sqrt{5} \\ [/tex]
5) 3√5 × -2√5
[tex] - 3 \times 2 \sqrt{ {5}^{2} } [/tex]
[tex] - 6 \times 5[/tex]
→ -35
Step-by-step explanation:
1. √2*√8=√2*8=√16=4
3.√8/√2=√8/2=√4=2
2.√125*√5=√125*5=√625=25
4.16√10/4√2=16/4√10/2=4√5
5.3√5*-2√5=3*-2(√5)²=-6*5=-30
Copyright © 2024 EHUB.TIPS team's - All rights reserved.
Answers & Comments
Verified answer
Simplification -
1) √2 × √8
[tex] \sqrt{2 \times 8} \\ [/tex]
[tex] \sqrt{2 \times 2 \times 2 \times 2} [/tex]
[tex] \sqrt{ {2}^{2} \times {2}^{2} } \\ [/tex]
[tex]2 \times 2 = 4[/tex]
→ 4
2) √125 × √5
[tex] \sqrt{5 \times 5 \times 5} \times \sqrt{5} [/tex]
[tex] \sqrt{ {5}^{2} \times 5} \times \sqrt{5} \\ [/tex]
[tex]5 \sqrt{5 \times 5} [/tex]
[tex]5 \times 5 = 25 \\ [/tex]
→ 25
3) √8/√2
[tex] \frac{ \sqrt{2 \times 2 \times 2} }{ \sqrt{2} } \\ [/tex]
[tex] \frac{2 \sqrt{2} }{ \sqrt{2} } \\ [/tex]
[tex] = > 2 \\ [/tex]
4) 16√10/4√2
[tex] \frac{16 \sqrt{5 \times 2} }{4 \sqrt{2} } \\ [/tex]
[tex] \frac{4 \sqrt{5} \sqrt{2} }{ \sqrt{2} } \\ [/tex]
[tex] = > 4 \sqrt{5} \\ [/tex]
5) 3√5 × -2√5
[tex] - 3 \times 2 \sqrt{ {5}^{2} } [/tex]
[tex] - 6 \times 5[/tex]
→ -35
Step-by-step explanation:
1. √2*√8=√2*8=√16=4
3.√8/√2=√8/2=√4=2
2.√125*√5=√125*5=√625=25
4.16√10/4√2=16/4√10/2=4√5
5.3√5*-2√5=3*-2(√5)²=-6*5=-30