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505-555 (Easy)|   Algebra|      
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Manasvi1
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If √(13 - a√10) = √8 + √5, then find the value of a 27 May 2020, 07:09
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

15% (low)

Question Stats:

85% (01:30) correct 15% (02:21) wrong based on 130 sessions

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If \(\sqrt{13 - a√10} = \sqrt{8} + \sqrt{5}\), then find the value of a.

A) +5
B) -6
C) +6
D) -4
E) +7
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D
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If √(13 - a√10) = √8 + √5, then find the value of a 27 May 2020, 08:50
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Manasvi1
\(If \sqrt{13 - a√10} = \sqrt{8} + \sqrt{5}\), then find the value of a.

A) +5
B) -6
C) +6
D) -4
E) +7
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Squaring both sides

13-a√10 = 8+5+2*√8*√5

i.e. \(13-a√10 = 13+2*√8*√5\)

i.e. \(-a√10 = 2*√40\)

i.e. \(a = -2*√4 = -4\)

ANswer: Option D
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If √(13 - a√10) = √8 + √5, then find the value of a 31 May 2020, 11:26
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Manasvi1
If \(\sqrt{13 - a√10} = \sqrt{8} + \sqrt{5}\), then find the value of a.

A) +5
B) -6
C) +6
D) -4
E) +7
Show more

Solution:

Squaring both sides, we have:

13 - a√10 = 8 + 5 + 2√40

-a√10 = 2√40

-a = 2√4

-a = 4

a = -4

Answer: D
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If √(13 - a√10) = √8 + √5, then find the value of a 20 Jun 2020, 21:58
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ScottTargetTestPrep
Manasvi1
If \(\sqrt{13 - a√10} = \sqrt{8} + \sqrt{5}\), then find the value of a.

A) +5
B) -6
C) +6
D) -4
E) +7

Solution:

Squaring both sides, we have:

13 - a√10 = 8 + 5 + 2√40

-a√10 = 2√40

-a = 2√4

-a = 4

a = -4

Answer: D
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Would you please explain this part?

13 - a√10 = 8 + 5 + 2√40

Thanks. :)
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If √(13 - a√10) = √8 + √5, then find the value of a 20 Jun 2020, 22:15
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Manasvi1
If \(\sqrt{13 - a√10} = \sqrt{8} + \sqrt{5}\), then find the value of a.

A) +5
B) -6
C) +6
D) -4
E) +7
Show more

Square both sides..
\((\sqrt{13 - a√10})^2=(\sqrt{8} + \sqrt{5})^2\),

\(13 - a√10= \sqrt{8}^2 + \sqrt{5}^2+2*\sqrt{8}*\sqrt{5}=8+5+2\sqrt{40}=13+2\sqrt{40}\),

\(13-a\sqrt{10}=13+2\sqrt{40}=13+4\sqrt{10}\)

\(-a\sqrt{10}=4\sqrt{10}.........a=-4\)

OR

Make use of choices...
5, 6 and 7 can be eliminated, as the LHS will became imaginary number - squareroot of a negative number.
Now \( RHS=\sqrt{8} + \sqrt{5} \)~\(3+2=5\\
\)
\(a=-6..LHS=\sqrt{13 - a√10}=\sqrt{13 +6√10}\)~\(\sqrt{13+18}\)~6...NO
\(a=-4..LHS=\sqrt{13 - a√10}=\sqrt{13 +4√10}\)~\(\sqrt{13+12}\)~5...YES

D
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If √(13 - a√10) = √8 + √5, then find the value of a 20 Jun 2020, 22:36
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Squaring both sides we get
13- a root(10) = 13+4 root(10)
Comparing both sides we get
a = -4

OA - D

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If √(13 - a√10) = √8 + √5, then find the value of a 03 Jul 2020, 12:09
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(13−a√10) = (√8+√5)^2
13−a√10 = 8+5+2√40
a√10 = 13-13-2√40
a√10 = -2√40
a = -4
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If √(13 - a√10) = √8 + √5, then find the value of a 12 Jul 2020, 15:08
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RajDev95
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Manasvi1
If \(\sqrt{13 - a√10} = \sqrt{8} + \sqrt{5}\), then find the value of a.

A) +5
B) -6
C) +6
D) -4
E) +7

Solution:

Squaring both sides, we have:

13 - a√10 = 8 + 5 + 2√40

-a√10 = 2√40

-a = 2√4

-a = 4

a = -4

Answer: D

Would you please explain this part?

13 - a√10 = 8 + 5 + 2√40

Thanks. :)
Show more

Explanation:

We are simply squaring each side of the equation √(13 - a√10) = √8 + √5.

The square of √(13 - a√10) is 13 - a√10. Tio find the square of √8 + √5, we have to FOIL (√8 + √5)(√8 + √5) to get:

(√8 + √5)^2

(√8)^2 + 2(√8)(√5) + (√5)^2

8 + 2√40 + 5

8 + 5 + 2√20
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If √(13 - a√10) = √8 + √5, then find the value of a 04 Feb 2022, 10:38
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