Answer:
[tex]( 3\sqrt{ {5}^{2} } - 6 \sqrt{2} )(4 \sqrt{ {5}^{2} } + 3 \sqrt{2} )[/tex]
[tex](3 \times 5 - 6 \sqrt{2} )(4 \times 5 + 3 \sqrt{2} )[/tex]
[tex]3(5 - \sqrt{2} )(20 + 3 \sqrt{2} )[/tex]
[tex]3(100 + 15 \sqrt{2} - 20 \sqrt{2} - 3 \sqrt{2} \times \sqrt{2} )[/tex]
[tex]3(100 + 15 \sqrt{2} - 20 \sqrt{2} - 3(2))[/tex]
[tex]3(100 + 15 \sqrt{2} - 20 \sqrt{2} - 6)[/tex]
[tex]3(94 - 5 \sqrt{2} )[/tex]
Step-by-step explanation: To solve the given expression, we can use the following steps:
Simplify the radicals.
3 sqrt 5^ 2 = 3 sqrt 25 = 15
4sqrt5 ^2 = 4 sqrt 25 = 20
Rewrite the expression using the distributive property.
(15 - 6 sqrt 2) (20 + 3sqrt 2) = 15(20) + 15(3sqrt 2) - 6 sqrt 2(20) - 6 sqrt 2(3sqrt 2) = 300 + 45sqrt 2 - 120 sqrt 2 - 18
Combine like terms.
300 + 45sqrt 2 - 120 sqrt 2 - 18 = 282 - 75sqrt 2
Conclusion
The simplified value of the expression (3 sqrt 5^ 2 -6 sqrt 2 ) (4sqrt5 ^2 + 3sqrt 2) is 282 - 75sqrt 2.
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Answers & Comments
Answer:
[tex]( 3\sqrt{ {5}^{2} } - 6 \sqrt{2} )(4 \sqrt{ {5}^{2} } + 3 \sqrt{2} )[/tex]
[tex](3 \times 5 - 6 \sqrt{2} )(4 \times 5 + 3 \sqrt{2} )[/tex]
[tex]3(5 - \sqrt{2} )(20 + 3 \sqrt{2} )[/tex]
[tex]3(100 + 15 \sqrt{2} - 20 \sqrt{2} - 3 \sqrt{2} \times \sqrt{2} )[/tex]
[tex]3(100 + 15 \sqrt{2} - 20 \sqrt{2} - 3(2))[/tex]
[tex]3(100 + 15 \sqrt{2} - 20 \sqrt{2} - 6)[/tex]
[tex]3(94 - 5 \sqrt{2} )[/tex]
Answer:
Step-by-step explanation: To solve the given expression, we can use the following steps:
Simplify the radicals.
3 sqrt 5^ 2 = 3 sqrt 25 = 15
4sqrt5 ^2 = 4 sqrt 25 = 20
Rewrite the expression using the distributive property.
(15 - 6 sqrt 2) (20 + 3sqrt 2) = 15(20) + 15(3sqrt 2) - 6 sqrt 2(20) - 6 sqrt 2(3sqrt 2) = 300 + 45sqrt 2 - 120 sqrt 2 - 18
Combine like terms.
300 + 45sqrt 2 - 120 sqrt 2 - 18 = 282 - 75sqrt 2
Conclusion
The simplified value of the expression (3 sqrt 5^ 2 -6 sqrt 2 ) (4sqrt5 ^2 + 3sqrt 2) is 282 - 75sqrt 2.